File "SL-paper2.html"

Path: /IB QUESTIONBANKS/5 Fifth Edition - PAPER/HTML/Math AA/Topic 4/SL-paper2html
File size: 949.88 KB
MIME-type: text/html
Charset: utf-8

 
Open Back
<!DOCTYPE html>
<html>


<meta http-equiv="content-type" content="text/html;charset=utf-8">
<head>
<meta charset="utf-8">
<title>IB Questionbank</title>
<link rel="stylesheet" media="all" href="css/application-02ef852527079acf252dc4c9b2922c93db8fde2b6bff7c3c7f657634ae024ff1.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-9717ccaf4d6f9e8b66ebc0e8784b3061d3f70414d8c920e3eeab2c58fdb8b7c9.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">

</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../../../../../../index.html">Home</a>
</li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Help
<b class="caret"></b>
</a>
<ul class="dropdown-menu">
<li><a href="https://questionbank.ibo.org/video_tour?locale=en">Video tour</a></li>
<li><a href="https://questionbank.ibo.org/instructions?locale=en">Detailed instructions</a></li>
<li><a target="_blank" href="https://ibanswers.ibo.org/">IB Answers</a></li>
</ul>
</li>
<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>

<div class="page-content container">
<div class="row">
<div class="span24">

<div class="pull-right screen_only"><a class="btn btn-small btn-info" href="https://questionbank.ibo.org/updates?locale=en">Updates to Questionbank</a></div>
<p class="muted language_chooser">
User interface language:
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=en">English</a>
|
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=es">Español</a>
</p>
</div>
</div>

<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="https://mirror.ibdocs.top/qb.png" alt="Ib qb 46 logo">
</div>
</div>
</div>
<h2>SL Paper 2</h2><div class="specification">
<p>A water container is made in the shape of a cylinder with internal height <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
  <mi>h</mi>
</math></span> cm and internal base radius <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span> cm.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p>The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>

<div class="specification">
<p>The volume of the water container is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.5{\text{ }}{{\text{m}}^3}">
  <mn>0.5</mn>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>m</mtext>
      </mrow>
      <mn>3</mn>
    </msup>
  </mrow>
</math></span>.</p>
</div>

<div class="specification">
<p>The water container is designed so that the area to be coated is minimized.</p>
</div>

<div class="specification">
<p>One can of water-resistant material coats a surface area of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="2000{\text{ c}}{{\text{m}}^2}">
  <mn>2000</mn>
  <mrow>
    <mtext>&nbsp;c</mtext>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>m</mtext>
      </mrow>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a formula for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>, the surface area to be coated.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Express this volume in <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{c}}{{\text{m}}^3}"> <mrow> <mtext>c</mtext> </mrow> <mrow> <msup> <mrow> <mtext>m</mtext> </mrow> <mn>3</mn> </msup> </mrow> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, in terms of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h"> <mi>h</mi> </math></span>, an equation for the volume of this water container.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A = \pi {r^2} + \frac{{1\,000\,000}}{r}"> <mi>A</mi> <mo>=</mo> <mi>π</mi> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> <mspace width="thinmathspace"></mspace> <mn>000</mn> </mrow> <mi>r</mi> </mfrac> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{d}}A}}{{{\text{d}}r}}"> <mfrac> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>A</mi> </mrow> <mrow> <mrow> <mtext>d</mtext> </mrow> <mi>r</mi> </mrow> </mfrac> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using your answer to part (e), find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r"> <mi>r</mi> </math></span> which minimizes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="A"> <mi>A</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the least number of cans of water-resistant material that will coat the area in part (g).</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows a probability distribution for the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span>, where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{E}}(X) = 1.2">
  <mrow>
    <mtext>E</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mi>X</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mn>1.2</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.18.09.png" alt="M17/5/MATME/SP2/ENG/TZ2/10"></p>
</div>

<div class="specification">
<p>A bag contains white and blue marbles, with at least three of each colour. Three marbles are drawn from the bag, without replacement. The number of blue marbles drawn is given by the random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span>.</p>
</div>

<div class="specification">
<p>A game is played in which three marbles are drawn from the bag of ten marbles, without replacement. A player wins a prize if three white marbles are drawn.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="q"> <mi>q</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability of drawing three blue marbles.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the probability of drawing three white marbles is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{6}"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The bag contains a total of ten marbles of which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w"> <mi>w</mi> </math></span> are white. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w"> <mi>w</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Jill plays the game nine times. Find the probability that she wins exactly two prizes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Grant plays the game until he wins two prizes. Find the probability that he wins his second prize on his eighth attempt.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the probability distribution of a discrete random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span>, where&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a \geqslant 0">
  <mi>a</mi>
  <mo>⩾<!-- ⩾ --></mo>
  <mn>0</mn>
</math></span> and&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b \geqslant 0">
  <mi>b</mi>
  <mo>⩾<!-- ⩾ --></mo>
  <mn>0</mn>
</math></span>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b = 0.3 - a"> <mi>b</mi> <mo>=</mo> <mn>0.3</mn> <mo>−</mo> <mi>a</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the difference between the greatest possible expected value and the least possible expected value.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The time it takes Suzi to drive from home to work each morning is normally distributed with a&nbsp;mean of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn></math> minutes and a standard deviation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#963;</mi></math> minutes.</p>
<p>On <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>%</mo></math>&nbsp;of days, it takes Suzi longer than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math> minutes to drive to work.</p>
</div>

<div class="specification">
<p>Suzi will be late to work if it takes her longer than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math> minutes to drive to work. The time it&nbsp;takes to drive to work each day is independent of any other day.</p>
<p>Suzi will work five days next week.</p>
</div>

<div class="specification">
<p>Suzi will work <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn></math> days this month. She will receive a bonus if she is on time at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> of&nbsp;those days.</p>
<p>So far this month, she has worked <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math> days and been on time <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> of those days.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On a randomly selected day, find the probability that Suzi’s drive to work will take longer than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math> minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that she will be late to work at least one day next week.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that Suzi will be late to work at least one day next week, find the probability that she will be late less than three times.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Suzi will receive a bonus.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows values of ln <em>x</em> and ln <em>y</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The relationship between ln <em>x</em> and ln <em>y</em> can be modelled by the regression equation ln <em>y</em> = <em>a</em> ln <em>x</em> + <em>b</em>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</em> and of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation to estimate the value of <em>y</em> when<em> x</em> = 3.57.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The relationship between <em>x</em> and <em>y</em> can be modelled using the formula <em>y</em> = <em>kx<sup>n</sup></em>, where <em>k</em> ≠ 0 , <em>n</em> ≠ 0 , <em>n</em> ≠ 1.</p>
<p>By expressing ln <em>y</em> in terms of ln <em>x</em>, find the value of <em>n</em> and of <em>k</em>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>In a group of 35 students, some take art class (<em>A</em>) and some take music class (<em>M</em>). 5 of these&nbsp;students do not take either class. This information is shown in the following Venn diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>One student from the group is chosen at random. Find the probability that</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of students in the group who take art class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the student does not take art class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the student takes either art class or music class, but not both.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The marks obtained by nine Mathematical Studies SL students in their projects (<em>x</em>) and their final IB examination scores (<em>y</em>) were recorded. These data were used to determine whether the project mark is a good predictor of the examination score. The results are shown in the table.</p>
<p><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The equation of the regression line <em>y</em> on <em>x</em> is <em>y</em> = <em>mx</em> + <em>c</em>.</p>
</div>

<div class="specification">
<p>A tenth student, Jerome, obtained a project mark of 17.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar x}">
  <mrow>
    <mrow>
      <mover>
        <mi>x</mi>
        <mo stretchy="false">¯</mo>
      </mover>
    </mrow>
  </mrow>
</math></span>, the mean project mark.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
  <mrow>
    <mrow>
      <mover>
        <mi>y</mi>
        <mo stretchy="false">¯</mo>
      </mover>
    </mrow>
  </mrow>
</math></span>, the mean examination score.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to write down <em>r </em>, Pearson’s product–moment correlation coefficient.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the exact value of <em>m</em> and of <em>c</em> for these data.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the point M (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar x}">
  <mrow>
    <mrow>
      <mover>
        <mi>x</mi>
        <mo stretchy="false">¯</mo>
      </mover>
    </mrow>
  </mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
  <mrow>
    <mrow>
      <mover>
        <mi>y</mi>
        <mo stretchy="false">¯</mo>
      </mover>
    </mrow>
  </mrow>
</math></span>) lies on the regression line <em>y</em> on <em>x</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression line <em>y</em> on <em>x</em> to estimate Jerome’s examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Justify whether it is valid to use the regression line y on x to estimate Jerome’s examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In his final IB examination Jerome scored 65.</p>
<p>Calculate the percentage error in Jerome’s estimated examination score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Emlyn plays many games of basketball for his school team. The number of minutes he plays in each game follows a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> minutes.</p>
<p>In any game there is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo> </mo><mo>%</mo></math> chance he will play less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>6</mn><mo>&nbsp;</mo><mtext>minutes</mtext></math>.</p>
</div>

<div class="specification">
<p>In any game there is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo> </mo><mo>%</mo></math> chance he will play less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>.</mo><mn>8</mn><mo>&nbsp;</mo><mtext>minutes</mtext></math>.</p>
</div>

<div class="specification">
<p>The standard deviation of the number of minutes Emlyn plays in any game is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math>.</p>
</div>

<div class="specification">
<p>There is a <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo> </mo><mo>%</mo></math> chance Emlyn plays less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> minutes in a game.</p>
</div>

<div class="specification">
<p>Emlyn will play in two basketball games today.</p>
</div>

<div class="specification">
<p>Emlyn and his teammate Johan each practise shooting the basketball multiple times from&nbsp;a point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>. A record of their performance over the weekend is shown in the table below.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>On Monday, Emlyn and Johan will practise and each will shoot <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math> times from point <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a diagram to represent this information.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>15</mn><mo>.</mo><mn>7</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Emlyn plays between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mtext>minutes</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mtext>minutes</mtext></math> in a game.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Emlyn plays more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>minutes</mtext></math> in a game.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability he plays between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo> </mo><mtext>minutes</mtext></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mtext>minutes</mtext></math> in one game and more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mtext>minutes</mtext></math> in the other game.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected number of successful shots Emlyn will make on Monday, based on the results from Saturday and Sunday.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Emlyn claims the results from Saturday and Sunday show that his expected number of successful shots will be more than Johan’s.</p>
<p>Determine if Emlyn’s claim is correct. Justify your reasoning.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>On a school excursion, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> students visited an amusement park. The amusement park’s&nbsp;main attractions are rollercoasters (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">R</mtext></math>), water slides (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">W</mtext></math>), and virtual reality rides (<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">V</mtext></math>).</p>
<p>The students were asked which main attractions they visited. The results are shown in the&nbsp;Venn diagram.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A total of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn></math> students visited the rollercoasters or the water slides.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students who visited at least two types of main attraction.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>(</mo><mo> </mo><mi>R</mi><mo>∩</mo><mi>W</mi><mo>)</mo><mo> </mo></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly selected student visited the rollercoasters.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly selected student visited the virtual reality rides.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence determine whether the events in <strong>parts (d)(i)</strong> and <strong>(d)(ii)</strong> are independent. Justify your reasoning. </p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>At a school, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn><mo>%</mo></math> of the students play a sport and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>%</mo></math> of the students are involved in&nbsp;theatre. <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>%</mo></math> of the students do neither activity.</p>
<p>A student is selected at random.</p>
</div>

<div class="specification">
<p>At the school <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>48</mn><mo>%</mo></math> of the students are girls, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>%</mo></math> of the girls are involved in theatre.</p>
<p>A student is selected at random. Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> be&nbsp;the event &ldquo;the student is a girl&rdquo; and let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> be the&nbsp;event &ldquo;the student is involved in theatre&rdquo;.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the student plays a sport and is involved in theatre.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the student is involved in theatre, but does not play a sport.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>G</mi><mo>∩</mo><mi>T</mi></mrow></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine if the events <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> are independent. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<p>The heights of adult males in a country are normally distributed with a mean of 180 cm and a standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma {\text{ cm}}">
  <mi>σ</mi>
  <mrow>
    <mtext> cm</mtext>
  </mrow>
</math></span>. 17% of these men are shorter than 168 cm. 80% of them have heights between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(192 - h){\text{ cm}}">
  <mo stretchy="false">(</mo>
  <mn>192</mn>
  <mo>−</mo>
  <mi>h</mi>
  <mo stretchy="false">)</mo>
  <mrow>
    <mtext> cm</mtext>
  </mrow>
</math></span> and 192 cm.</p>
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="h">
  <mi>h</mi>
</math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the average body weight, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>, and the average weight of the brain, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>, of seven species of mammal. Both measured in kilograms (kg).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_10.57.27.png" alt="M17/5/MATSD/SP2/ENG/TZ1/01"></p>
</div>

<div class="specification">
<p>The average body weight of grey wolves is 36 kg.</p>
</div>

<div class="specification">
<p>In fact, the average weight of the brain of grey wolves is 0.120 kg.</p>
</div>

<div class="specification">
<p>The average body weight of mice is 0.023 kg.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the range of the average body weights for these seven species of mammal.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the data from these seven species calculate <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span>, the Pearson’s product–moment correlation coefficient;</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For the data from these seven species describe the correlation between the average body weight and the average weight of the brain.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>, in the form <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = mx + c">
  <mi>y</mi>
  <mo>=</mo>
  <mi>m</mi>
  <mi>x</mi>
  <mo>+</mo>
  <mi>c</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your regression line to estimate the average weight of the brain of grey wolves.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the percentage error in your estimate in part (d).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether it is valid to use the regression line to estimate the average weight of the brain of mice. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>At Penna Airport the probability, P(<em>A</em>), that all passengers arrive on time for a flight is 0.70. The probability, P(<em>D</em>), that a flight departs on time is 0.85. The probability that all passengers arrive on time for a flight and it departs on time is 0.65.</p>
</div>

<div class="specification">
<p>The number of hours that pilots fly per week is normally distributed with a mean of 25 hours and a standard deviation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
  <mi>σ<!-- σ --></mi>
</math></span>. 90 % of pilots fly less than 28 hours in a week.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that event <em>A</em> and event <em>D</em> are <strong>not</strong> independent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}\left( {A \cap D'} \right)">
  <mrow>
    <mtext>P</mtext>
  </mrow>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>A</mi>
      <mo>∩</mo>
      <msup>
        <mi>D</mi>
        <mo>′</mo>
      </msup>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p> Given that all passengers for a flight arrive on time, find the probability that the flight does <strong>not</strong> depart on time.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
  <mi>σ</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>All flights have two pilots. Find the percentage of flights where <strong>both</strong> pilots flew more than 30 hours last week.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The table below shows the distribution of test grades for 50 IB students at Greendale School.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_11.25.22.png" alt="M17/5/MATSD/SP2/ENG/TZ1/05"></p>
</div>

<div class="specification">
<p>A student is chosen at random from these 50 students.</p>
</div>

<div class="specification">
<p>A second student is chosen at random from these 50 students.</p>
</div>

<div class="specification">
<p>The number of minutes that the 50 students spent preparing for the test was normally distributed with a mean of 105 minutes and a standard deviation of 20 minutes.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the mean test grade of the students;</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the standard deviation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the median test grade of the students.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the interquartile range.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student scored a grade 5 or higher.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the first student chosen at random scored a grade 5 or higher, find the probability that both students scored a grade 6.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability that a student chosen at random spent at least 90 minutes preparing for the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected number of students that spent at least 90 minutes preparing for the test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>In the month before their IB Diploma examinations, eight male students recorded the number of hours they spent on social media.</p>
<p>For each student, the number of hours spent on social media (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>) and the number of IB Diploma points obtained (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>) are shown in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_07.43.52.png" alt="N16/5/MATSD/SP2/ENG/TZ0/01"></p>
</div>

<div class="specification">
<p>Use your graphic display calculator to find</p>
</div>

<div class="specification">
<p>Ten female students also recorded the number of hours they spent on social media in the month before their IB Diploma examinations. Each of these female students spent between 3 and 30 hours on social media.</p>
<p>The equation of the regression line <em>y </em>on <em>x </em>for these ten female students is</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="y = &nbsp;- \frac{2}{3}x + \frac{{125}}{3}.">
  <mi>y</mi>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mfrac>
    <mn>2</mn>
    <mn>3</mn>
  </mfrac>
  <mi>x</mi>
  <mo>+</mo>
  <mfrac>
    <mrow>
      <mn>125</mn>
    </mrow>
    <mn>3</mn>
  </mfrac>
  <mo>.</mo>
</math></span></p>
<p>An eleventh girl spent 34 hours on social media in the month before her IB Diploma examinations.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-axis and 2 cm to represent 10 points on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>-axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i)     <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar x}">
  <mrow>
    <mrow>
      <mover>
        <mi>x</mi>
        <mo stretchy="false">¯</mo>
      </mover>
    </mrow>
  </mrow>
</math></span>, the mean number of hours spent on social media;</p>
<p>(ii)     <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\bar y}">
  <mrow>
    <mrow>
      <mover>
        <mi>y</mi>
        <mo stretchy="false">¯</mo>
      </mover>
    </mrow>
  </mrow>
</math></span>, the mean number of IB Diploma points.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="(\bar x,{\text{ }}\bar y)">
  <mo stretchy="false">(</mo>
  <mrow>
    <mover>
      <mi>x</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
  <mo>,</mo>
  <mrow>
    <mtext> </mtext>
  </mrow>
  <mrow>
    <mover>
      <mi>y</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
  <mo stretchy="false">)</mo>
</math></span> on your scatter diagram and label this point M.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span>, the Pearson’s product–moment correlation coefficient, for these data.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> for these eight male students.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line, from part (e), on your scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down a reason why this estimate is not reliable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A manufacturer produces 1500 boxes of breakfast cereal every day.</p>
<p>The weights of these boxes are normally distributed with a mean of 502 grams and a standard deviation of 2 grams.</p>
</div>

<div class="specification">
<p>All boxes of cereal with a weight between 497.5 grams and 505 grams are sold. The manufacturer’s income from the sale of each box of cereal is $2.00.</p>
</div>

<div class="specification">
<p>The manufacturer recycles any box of cereal with a weight <strong>not </strong>between 497.5 grams and 505 grams. The manufacturer’s recycling cost is $0.16 per box.</p>
</div>

<div class="specification">
<p>A <strong>different </strong>manufacturer produces boxes of cereal with weights that are normally distributed with a mean of 350 grams and a standard deviation of 1.8 grams.</p>
<p>This manufacturer sells all boxes of cereal that are above a minimum weight, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
  <mi>w</mi>
</math></span>.</p>
<p>They sell 97% of the cereal boxes produced.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a diagram that shows this information.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>(i)     Find the probability that a box of cereal, chosen at random, is sold.</p>
<p>(ii)     Calculate the manufacturer’s expected daily income from these sales.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the manufacturer’s expected daily recycling cost.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
  <mi>w</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The final examination results obtained by a group of 3200 Biology students are summarized on the cumulative frequency graph.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAk4AAALSCAYAAAAr/V7NAAAgAElEQVR4AezdC3gU1fk/8G+CImhErj9NAEXABBQKAglU0HIziBeCIGJREwv0r2LRwo8QglJbERBCQxVR+5NQg4qCEkhr5VKIIEEgJISLAonhooREColcIkEkO//nLNmw2d1kTiazuzOz330em92ZM+e87+cM9DAzeTdIURQFfFGAAhSgAAUoQAEKqAoEq7ZgAwpQgAIUoAAFKEABuwAXTjwRKEABClCAAhSggKQAF06SUGxGAQpQgAIUoAAFuHDiOUABClCAAhSgAAUkBbhwkoRiMwpQgAIUoAAFKMCFk97nQHEa4oKCECT+G7AAOWW2yyOczUBCWFeMS/sOlVv0Hpn9UYACFKAABSjgZQEunPQGDh2BVKUceSmjgE3bsKfo4uURQiIw5KlbUHi6XO8R2R8FKEABClCAAj4S4MLJK9CN0L5bFDrgJErPXbo8QnALtOl4B+7tdhOI7hV0dkoBClCAAhTwugD/P9xLxMHXN0cHHMO+7360j2A7/jmSs3rjt3c29dKI7JYCFKAABShAAW8LcOHkJeHg65vipqq+TyN3RT6iZzyI1hSvUuEbClCAAhSggNkE+H/j3pqx65riptBD2Hr4exzLWIyVt/wWw1s39NZo7JcCFKAABShAAR8IcOHkLeRrb0Cra4HzuUvwt03dMHH4LXy2yVvW7JcCFKAABSjgIwEunLwFHXwdmncIBa66B7+fOgihlPaWNPulAAUoQAEK+EyA/3fuTeo2z+GD136LTiFk9iYz+6YABShAAQr4SoD/j+4V6dPIeX05ED8RA0Pdn2t68803kZ+f75WR2SkFKEABClCAAt4TCFIURfFe94HU82nkzH8CDxWPwD/aHMX+eyZjUk/30gOFhYVo27Ytxo8fj3fffTeQgJgrBShAAQpQwPQCvOKk2xRewpmTP6B4Vx5+uOdZvOBh0SSGeuONN+wjLl68GOvXr9dtdHZEAQpQgAIUoID3BXjFyfvGVSNs3boV/fr1s39OTU2FuGW3efNmNG7cuKoN31CAAhSgAAUoYFwBXnHy0dyUl5cjKSkJCxcutI84atQo+89PPvnERxFwGApQgAIUoAAF6ivAhVN9BSWPX7NmDYqKijBu3Dj7EeIq04IFCxAXF4fS0lLJXtiMAhSgAAUoQAF/CvBWnQ/0xcLovvvuw7Rp0zBixAgEBQXB8Uz+73//ezRr1gzz5s3zQSQcggIUoAAFKECB+ghw4VQfPcljZ8+ejaysLKxevdp+hPPCSZQliIiIQF5eHsLDwyV7ZDMKUIACFKAABfwhwIWTl9UdC6Pc3Fx0797dPprzwklscF1YeTkkdk8BClCAAhSggEaBqzQex8MkBVq2bAnxG3SORZOnw5555hl06tTJ0y5uowAFKEABClDAQAK84uSHyXC94uSHEDgkBShAAQpQgAIaBPhbdRrQeAgFKEABClCAAoEpwIVTYM47s6YABShAAQpQQIMAF04a0HgIBShAAQpQgAKBKcCFU2DOO7OmAAUoQAEKUECDABdOGtB4CAUoQAEKUIACgSnAhVNgzjuzpgAFKEABClBAgwAXThrQeAgFKEABClCAAoEpwIVTYM47s6YABShAAQpQQIMAF04a0HgIBShAAQpQgAKBKcCFU2DOO7OmAAUoQAEKUECDABdOGtB4CAUoQAEKUIACgSnAhVNgzjuzpgAFKEABClBAgwAXThrQeAgFKEABClCAAoEpwIVTYM47s6YABShAAQpQQIMAF04a0HgIBShAAQpQgAKBKcCFU2DOO7OmAAUoQAEKUECDABdOGtB4CAUoQAEKUIACgSlgroWTrRhZC+IQFhSEoKAhSEg7iDKP83YKGQm9EGRvJ9qGYciSg7A5tbUVZyE1YYi9TVjcImQVX3Tae/mtTBu3g7iBAhSgAAUoQAHLCpho4XQauau3Ao+9iyLlZxTtGIYf/vAEZmaccpsc2/Ev8eH7OU7b+2F0v3aoSrYsC8ljXkHekCWoUH5GTtwpJIxZhJwyp6WVTBunEfiWAhSgAAUoQAHrC1StJYyequ3QNzjTexiiQhsCaIjQqNGIexJ4f91enK0W/GnkfpSOlh+chKIolf+twNjwRpWtLiB/xXwkR03GtIGtESz6GvgcZkR9iukr8iuvSsm0qTYoP1CAAhSgAAUoEAACplk4BXfoi/6txaKp8mU7haO722Lyoz3QxLFN/Dy7CyuSl2LezCQsSduEfOerSGK/7Sgyl+9C14gwhFQd1xy9hvwG+5Z/hQJx0UmmTdWxfEMBClCAAhSgQKAImGbhdGVCbCjLz8CSxL+hIOFNTO7Z9MouXED+p+9gXjGATfMwbuQARDz0EtLyr1yTshV8heXrm6J7u5ZXbt05eli/FpkFFyDTxnEIf1KAAhSgAAUoEDgCJls4iYe+o3B9xCCMm/dPbFu3AwXVrig1QvjYFVDEM1DZ/0LK1Ghg0xyMfDql8vklG8oKC7AP7RHR5sr1purTLdOm+hH8RAEKUIACFKBAYAiYbOHUEgPnZkOpKEL2e08C80ai/wurcdzpme7L09YQoT0fxNi5/0LRxj+j/6YPsSKrNDBmlFlSgAIUoAAFKOA1gau81rM3Ow4ORc+4v+DvFUcQ8VI28sqGo3UTT2vAyge/p/4LT6zbixcHDkRIm47oivXIKywDqh4Ydw42WKKNc3vP73v37u15B4CoqCjUtr/GA7mDAhSgAAUoYACBHTt2GCAKP4WgmPhVkZeiRIcmKhvPVNSSRbmSlzJGiU45oNhbVRxQUqLvUqZuPOl0jGgzSkF0ipInGsm0cTq6rm8B8ct+tb9WrVpVawO1/eJgtTYlJSXK1q1bax0nKiqq1v16jaMWq8w4BQUFyl/+8pda49VjHBk3mXHUbPPz8xXxX20vmXHU2siMoxarzPzItFGLVaYPM8Uq8lGLVw8TPfrwVawycyyTj5qrXuPIxKLWRo9YfZmPTLwiHqu+PF2m8dMSrq7DXn4W6dDQXogIqS2NMhQWdEXCI+GXHwYPbod+o1u7lDEoQ2HecUSPvgsdRVcybeoaLttTgAIUoAAFKGB6gdpWHAZK7iKOp/0BYQMSkJpTbK+1ZCveiNfmlmJ6/GC0dmRhK0ZO+ufIcVQBt1caT8amwU+if9WtvEYIf3QKJmcl47WM47DhIoozFmFm1iOY/Wjl4goybQzEw1AoQAEKUIACFPCJgGPJ4ZPBtA9yFW64PRL35s3DU73C0CCoK3734TmMfO8NjO3kXMXJhjM7XkevsGsQFNQVcclfouyBaXjFXujSafSQKExelohWqfehQVA7jFnXHvOXPYeezleuZNo4dcm3FKAABShAAQpYX8AkD4cHI6RTHFKL4pBa25wEt8bA2eugzK6t0eV9waF9MSl1HybV0qFMG/WR2IICFKAABShAAasImOSKk1W4mQcFKEABClCAAmYW4MLJzLPH2ClAAQpQgAIU8KkAF04+5eZgFKAABShAAQqYWSBI1FkwcwJmi3316tV4+OGHsWrVKlOEPmfOHCQmJpoi1hMnTmD79u2IiYkxRbxmsmWs3julaOsdW7p6x1X0KmxZANOqVaoMmhcLYLpPjFqBOHGEWhsWwHR3lXFjAUxtbmrno4y9aKNWTFCPcfTow1exyrjJ5KPmqtc4MrGotdEjVl/mIxOviMeqL96q896inD1TgAIUoAAFKGAxAS6cLDahTIcCFKAABShAAe8JcOHkPVv2TAEKUIACFKCAxQS4cLLYhDIdClCAAhSgAAW8J8CFk/ds2TMFKEABClCAAhYT4MLJYhPKdChAAQpQgAIU8J4AF07es2XPFKAABShAAQpYTIAFMH08oSyA6T1wFsD0ni2LCdJWCPA88M55YCZXx3nAAphWrVJl0LxYANN9YtQKxIkj1NqwAKa7q4wbC2Bqc1M7H2XsRRu1YoJ6jKNHH76KVcZNJh81V73GkYlFrY0esfoyH5l4RTxWffFWnXf+AcFeKUABClCAAhSwoAAXThacVKZEAQpQgAIUoIB3BLhw8o4re6UABShAAQpQwIICXDhZcFKZEgUoQAEKUIAC3hHgwsk7ruyVAhSgAAUoQAELCnDhZMFJZUoUoAAFKEABCnhHgHWcvONaY6+s41QjTb13sI5TvQlr7MBMdWbMFKsAN1O8jLXGPyL12mEmV8c5yzpOVi22YNC8WMfJfWLU6pyII9TasI6Tu6uMG+s4aXNTOx9l7EUbtZo4eoyjRx++ilXGTSYfNVe9xpGJRa2NHrH6Mh+ZeEU8Vn3xVl29/p3AgylAAQpQgAIUCCQBLpwCabaZKwUoQAEKUIAC9RLgwqlefDyYAhSgAAUoQIFAEuDCKZBmm7lSgAIUoAAFKFAvAS6c6sXHgylAAQpQgAIUCCQBLpwCabaZKwUoQAEKUIAC9RLgwqlefDyYAhSgAAUoQIFAEmABTB/PNgtgeg+cBTC9Z2umAn1milXMmJniZaze+TNmJlfHOcsCmFatUmXQvFgA031i1ArEiSPU2rAAprurjBsLYGpzUzsfZexFG7VignqMo0cfvopVxk0mHzVXvcaRiUWtjR6x+jIfmXhFPFZ98Vadd/4BwV4pQAEKUIACFLCgABdOFpxUpkQBClCAAhSggHcEuHDyjit7pQAFKEABClDAggJcOFlwUpkSBShAAQpQgALeEeDCyTuu7JUCFKAABShAAQsKcOFkwUllShSgAAUoQAEKeEeAdZy844revXt7qWd2SwEKUIACFPCvAOs4WbXYgkHzYh0n94lRq3MijlBrwzpO7q4ybqzjpM1N7XyUsRdt1Gri6DGOHn34KlYZN5l81Fz1GkcmFrU2esTqy3xk4hXxWPXFW3X+XbRzdApQgAIUoAAFTCTAhZOJJouhUoACFKAABSjgXwEunPzrz9EpQAEKUIACFDCRABdOJposhkoBClCAAhSggH8FuHDyrz9HpwAFKEABClDARAJcOJloshgqBShAAQpQgAL+FWAdJz/4BwUFYdWqVX4Yue5DzpkzB4mJiXU/0A9HnDhxAtu3b0dMTIwfRq/7kGayZax1n1/ZI2grK1W3dnStm5en1kVFRfbNZ8+exenTp+3vCwsL8c033yA3N9fTIYGxzap1FoycF+s4uc+OWp0TcYRaG9ZxcneVcWMdJ21uauejjL1oo1YTR49x9OjDV7HKuMnko+aq1zgysai10SPWuuZz7NgxJS8vT1m3bp2ycuVKZdasWUp8fLz9fBT/H+X8X2RkpH2f2L9w4UKlR48eYriAfV0VGMtDZkkBClCAAhQILAFxdej8+fP4+uuvIa4ebdy4EbNnz8bOnTurIMQV+vDwcDRt2hR9+vRBcHAw3n//ffv+tm3bonHjxlVtHW8c+x2fA+0nF06BNuPMlwIUoAAFLCVQXl6OY8eO2R9VEIulPXv2YPHixVU5jh8/Hs2aNUNERASeffZZtGvXDi1btkTz5s2r2jjeiIWTWEjxVbMAF04123APBShAAQpQwHAC+fn59qtIBw8eRFZWFtLT0+0xDh48GE2aNMHQoUPx3HPP2RdHbdq0qYp/9erViI6OrvrMN9oEuHDS5sajKEABClCAAj4REAsl8YsvX331FZKSkuxjiltsYqE0YcIEzJs3z36VSCyMhg8f7pOYAnkQLpwCefaZOwUoQAEKGE5A3G7bv38/NmzYULVQEoukJ5980v7bbOKWm6dnjwyXiEUD4sLJohPLtChAAQpQwBwCNpsNW7dutS+KxGJJ3HpzXFESv/YvFkrr1q3j1SSDTCcXTgaZCIZBAQpQgAKBIyCuKonnk9asWYPs7Gz069cP8fHxiI2NxZtvvgnnZ5MCR8UcmbIAph/miQUwvYPOApjecRW9spggbXke1P8cKCkpwd69e+3PK4lFU1RUlL0EQEZGBmbOnFn/AXzUg/j7YMeOHT4azYDDBGwFKz8mzgKY7vhqBeLEEWptWADT3VXGjQUwtbmpnY8y9qKNWvFDPcbRow9fxSrjJpOPmqte46jFcv78eeXll19Wxo8fby8qGRMTo6SmpiqiAKXjpUesvspHjCMTryM3K/7krToDLmYZEgUoQAEKmFtA/Cbc+vXrMXHiRHTs2BEvvPCCvdYSb8GZe15F9Fw4mX8OmQEFKEABChhEQDzk/d5779kLUIrCk5mZmTh58iQf7DbI/OgRRrAenbAPClCAAhSgQCALiAWTqKEkHvLu1q0b8vLy8O6776Jv376BzGLJ3LlwsuS0MikKUIACFPCFgKje7VgwiVpL4gHwP/zhD/zaEl/g+2kMLpz8BM9hKUABClDAvAK7d++2L5gSExPtFbwdCyZP3/9m3iwZuScBLpw8qXAbBShAAQpQwIOAqL80depU3HnnnfYF09KlS+1XmLhg8oBl0U1cOFl0YpkWBShAAQroJ1BeXg6xSGrbtq29U/EMk7gld/311+s3CHsyhQALYPphmlgA0zvoLIDpHVfRKwtg0jaQz4MjR47grbfesp8E48aNQ6dOnXQ9Icz058txHrAAphUrVBk4JxbAdJ8ctSJy4gi1NiyA6e4q48YCmNrc1M5HGXvRRq2YoB7j6NGHr2KVcZPJR81VZpylS5cq8fHx9sKVomilKGbp+pKJRa2NHrHK5KMWh0wfoo1MvK5OVvrMOk66/ruBnVGAAhSggBUExMPfr7zyCu644w57aYHw8HArpMUcdBDgM046ILILClCAAhSwhoB4lmn27Nn2h7/vv/9+fPTRRywtYI2p1S0LXnHSjZIdUYACFKCAmQXEb8yJB76LioqQm5uLo0ePonHjxmZOibF7QYBXnLyAyi4pQAEKUMBcAuJ75cRvzIlbcps3b0b37t3NlQCj9ZkArzj5jJoDUYACFKCA0QTErbmUlBT7l/GuXLkSI0aMMFqIjMdgAlw4GWxCGA4FKEABCvhG4OLFi3j++eexZ88e+605XmXyjbvZR2EdJz/MIOs4eQeddZy84yp6NVOdGTPFSlv/nbPiK1Jee+01tGvXDo899hhatGjhvWBUejbjOcs6TlYqsGCCXFjHyX2S9KgvwjpO7q5ii5ot6zhpc1NzlbEXbdRq4ugxjh59+CpWGTeZfGpzzc3NVSIjI5Xhw4d7rM0kYhAvmXH0aFNbrJWh6BKLHrGKeGTidcRtxZ/mejjcVoysBXEICwpCUNAQJKQdRJmHlbytOAupCUMgruyExS1CVvFFt1Z6tXHrmBsoQAEKUMCwAlu3brWXGoiNjUVcXBx/a86wM2XcwEy0cDqN3NVbgcfeRZHyM4p2DMMPf3gCMzNOVdcty0LymFeQN2QJKpSfkRN3CgljFiGnzHalnV5trvTIdxSgAAUoYHAB8Ztz/fr1Q2pqqr3sgMHDZXgGFTDNwsl26Buc6T0MUaENATREaNRoxD0JvL9uL85W4V5A/or5SI6ajGkDWyNYtBv4HGZEfYrpK/JxeemkV5uqQfmGAhSgAAUMLvDmm29iyJAhyMzMhLjaxBcFtAqYZuEU3KEv+rcWi6bKl+0Uju5ui8mP9kCTqm1Hkbl8F7pGhCHEsQ3N0WvIb7Bv+VcoECsnm05tqvrnGwpQgAIUMLKAuNI0ceJE+6Kpb9++Rg6VsZlAwDQLpyuWNpTlZ2BJ4t9QkPAmJvdsWrXLVvAVlq9viu7tWsItsfVrkVlwAXq1qRqUbyhAAQpQwLAC4pkmx5UmLpoMO02mCsxtfWHs6E8hIyEK10cMwrh5/8S2dTtQUPXskg1lhQXYh/aIaHPlelP1fPRqU71XfqIABShAAeMJ5Ofn259pWrhwIbhoMt78mDUiky2cWmLg3GwoFUXIfu9JYN5I9H9hNY47Pfdt1olg3BSgAAUooJ+AKG75xBNPQCyaxPfP8UUBvQRMXADzAvKXxCLipY7YePBVDGwSDFv+EgyNeAvdN67F3IEtK41sOJvxEjoNKsCreUvxFJbp0mZseKNa56B379417s/KykJUVFSN+7mDAhSgAAW0C9hsNhw4cADXXnstbr31Vu0d8cgaBVgA06QVqiryUpTo0ERl45mKyxlUHFBSou9Spm486ZRRuZKXMkpBdIqSJ5rp1cZphLq+ZQFMdzE9CrOxAKa7q9iiZssCmNrc1Fxl7EUbtWKCeoyjRx++ilXGrbZ8zp8/r4wfP15p1apVrcUt6zuOOF68aoulsolqG7VzQK9x9IhVxCITryN3K/402a0658Xv5eeVDg3thYiQyjSC26Hf6NYuJQrKUJh3HNGj70JH0UyvNs6h8D0FKEABChhCYMGCBfbvnmvbti2LWxpiRqwXhEkWThdxPO0PCBuQgNScYns9JlvxRrw2txTT4wejdVUWjRD+6BRMzkrGaxnHYcNFFGcswsysRzD70fDK37TTq431TgZmRAEKUMDMAkuXLsWLL76ItLQ0XHUVv8PezHNp5NirlhxGDhK4CjfcHol78+bhqV5haBDUFb/78BxGvvcGxnaqquJ0OYWQKExelohWqfehQVA7jFnXHvOXPYeejqtSopVebYyNxugoQAEKBIyAKDsgvkJFFLhs06ZNwOTNRH0vYJIleTBCOsUhtSgOqRJGwaF9MSl1HybV0livNhLhsAkFKEABCnhRoLCwsOqrVFh2wIvQ7NouYJIrTpwtClCAAhSggLtAeXk5RowYgfj4eH6VijsPt3hBgAsnL6CySwpQgAIU8I3A888/j7CwMPzlL3/xzYAcJeAFTFzHybxzFxQUhFWrVpkigTlz5iAxMdEUsZ44cQLbt29HTEyMKeI1ky1j9d4pRVvttl988QU+//xzTJs2DS1atKjWEV2rcej6QdiyjpMVCy0YOCfWcXKfHD3qi7COk7ur2KJmyzpO2tzUXGXsRRu1mjh6jKNHH76KVcZN5JObm6uIv0szMzPFIW4vNVdxgJqL2n6ZPmTa6BGrzDh65SMTr4jHqi/eqtN1Hc7OKEABClDA2wIlJSX4f//v/9m/ToUPg3tbm/27CnDh5CrCzxSgAAUoYFgB8TD4xx9/jG7duvE76Aw7S9YOzCTlCKw9CcyOAhSgAAXkBFJSUnD06FEsX75c7gC2ooDOArzipDMou6MABShAAe8I7N69GxMnTsSECRPQvHlz7wzCXimgIsArTipA3E0BClCAAv4XKC0trXquiZXB/T8fgRwBrzgF8uwzdwpQgAImEXjttdfszzWNGzfOJBEzTKsK8IqTVWeWeVGAAhSwiID40t6kpCQcO3YMjRs3tkhWTMOsAiyA6YeZYwFM76CzAKZ3XEWvLCZIW3+dB6L0wPjx4/Hyyy+je/fu0hPBc1aaqs4NWQDTqhWqDJwXC2C6T44ehdlYANPdVWxRs2UBTG1uaq4y9qKNWjFBPcbRow9fxersdv78eWX8+PFKfHy82Fz1kslHzVV0ptaP2n6ZPmTa6BGrzDh65SMTr4jHqi/eqqvzWpsHUIACFKCALwQ++eQT7NmzB2vXrvXFcByDAlICXDhJMbERBShAAQr4UiA/Px9xcXFYt24dSw/4Ep5jqQrwt+pUidiAAhSgAAV8KXDx4kVMnToVs2bNQnR0tC+H5lgUUBXgwkmViA0oQAEKUMCXAlu3bkVRUREmTZrky2E5FgWkBHirToqJjShAAQpQwBcC4hbdG2+8gczMTJYe8AU4x6izAK841ZmMB1CAAhSggLcERL2m4cOHo2/fvt4agv1SoF4CrONULz5tB7OOkzY3taNYx0lNSPt+1sTRbqd2JG2vCG3fvh0rV67En/70J1x//fVXdmh4R1cNaJKHsI6TVQstGDgv1nFynxw96ouwjpO7q9iiZss6Ttrc1Fxl7EUbtZo4eoyjRx/ejrWkpEQRfzeuXLlS9ZyVyUfNVWZ+ZMbRo40esfoyH5l4RTxWffFWneQKm80oQAEKUMB7AuK76ESF8BEjRnhvEPZMAR0E+HC4DojsggIUoAAFtAuI36JzfBed9l54JAV8I8ArTr5x5igUoAAFKOBBoLy83F52IDU1FW3atPHQgpsoYCwBLpyMNR+MhgIUoEBACYivVRGvUaNGBVTeTNa8ArxVZ965Y+QUoAAFTC1QWFho/1oV1mwy9TQGXPC84hRwU86EKUABChhDQBS6jI+PZ80mY0wHo5AU4BUnSSg2owAFKEAB/QQcD4Tn5eXp1yl7ooAPBFgA0wfIrkOwAKariD6fWQBTH0dPvbCYoCcVfbYFoq34Et+//vWv6NatG+6//359IF16CURXFwKvfWQBTKtWqDJwXiyA6T45ehSRYwFMd1exRc2WBTC1uam5ytiLNmrFBPUYR48+9IxVFLmMjIxUzp8/7xFfLV61/TKxijZq/ajtl+lDpo3aOSDTh0wbvfKRiVfEY9UXb9V5bU3OjilAAQpQwFXg3LlzWLhwIaZNm8Yv8XXF4WdTCPDhcFNME4OkAAUoYA2BLVu2ICwsDEOHDrVGQswi4AR4xSngppwJU4ACFPCPQGlpKd59912w/IB//DmqPgK84qSPI3uhAAUoQAEVAfF9dIMHD2b5ARUn7ja2ABdOxp4fRkcBClDAEgL5+fn276N7+OGHLZEPkwhcAS6cAnfumTkFKEABnwksXrzYXuxSPN/EFwXMLMBnnMw8e4ydAhSggAkEdu/ebb/aJIpd7t+/3wQRM0QK1CzAApg129RrT+/evWs8PisrC1FRUTXu5w4KUIACVhL49ttv0aRJE9x4441WSiugc9mxY0fg5m/VAlVGzosFMN1nR4/CbCyA6e4qtqjZsgCmNjc1Vxl70UatmKAe4+jRh9ZYMzMzFfF3XklJiR1aj1hk+lBzlZkfmXH0aKNHrL7MRyZe+2Rb9H/4jFPgrpmZOQUoQAGvCyQlJdkLXjZv3tzrY3EACvhCgAsnXyhzDApQgAIBKCC+yDc9PR1jxowJwOyZslUFuHCy6swyLwpQgAJ+FuDVJj9PAIf3igAXTl5hZacUoAAFAluAV5sCe/6tnD0XTqO+HnwAACAASURBVFaeXeZGAQpQwE8CvNrkJ3gO63UBLpy8TswBKEABCgSWAK82BdZ8B1q2rOPkhxkPCgrCqlWr/DBy3YecM2cOEhMT636gH444ceIEtm/fjpiYGD+MXvchzWTLWOs+v7JHWNFW5NStWzfcf//9sgy6t7Oiq+5IGjsUtqzjZNFaC0ZNi3Wc3GdGj1oorOPk7iq2qNmyjpM2NzVXGXvRRq0mjh7j6NGHbKy5ubnV6ja56uoRi0wfaq4y8yMzjh5t9IjVl/nIxOs671b6zFt1GlfcPIwCFKAABdwFli1bhlmzZoF1m9xtuMUaAvyuOmvMI7OgAAUo4HeBoqKiqu+k83swDIACXhLgFScvwbJbClCAAoEm8J///Afx8fEIDw8PtNSZbwAJ8IpTAE02U6UABSjgLYHS0lKsXr0aeXl53hqC/VLAEAK84mSIaWAQFKAABcwtIJ5tioqK4tUmc08jo5cQ4MJJAolNKEABClCgZgFxtWnixIl4+OGHa27EPRSwiAAXThaZSKZBAQpQwF8CmzZtstdP69Spk79C4LgU8JkAC2D6jPrKQCyAecVCz3csgKmnZvW+WEywuoeen8xue/HiRbz44osYOXIk+vTpoydNvfoyu2u9kvfywSyAaaWqVCbJhQUw3SdKjyJyLIDp7iq2qNmyAKY2NzVXGXvRRq2YoB7j6NFHTbFmZmbaC16eP39e9VyTNVGLV21/TbGK7c4vtX7U9ou+9Gijdg7oNY4esYpYZOJ1drbae96q8/LKnN1TgAIUsLKA48t8GzdubOU0mRsFqgS4cKqi4BsKUIACFKiLQH5+PtLT0zFmzJi6HMa2FDC1ABdOpp4+Bk8BClDAfwKffvqpveAlv17Ff3PAkX0vwAKYvjfniBSgAAVMLyBKEIiHwjMzM02fCxOgQF0EeMWpLlpsSwEKUIACdoHPPvvMXoKgb9++FKFAQAlw4RRQ081kKUABCugj8OabbyI2NlafztgLBUwkwIWTiSaLoVKAAhQwgsDWrVuxc+dO9O/f3wjhMAYK+FSABTB9yn15MBbA9A46C2B6x1X0ymKCtHU+D1JTU9GqVSvcf//93oOpZ888Z+sJWMvhLIBptcpUJsiHBTDdJ0mPwmwsgOnuKrao2bIApjY3NVcZe9FGrZigHuPo0Ycj1pKSEnvBy7y8PDc4vcZR60dtvyNWtwBdNqj1o7ZfdKdHG7VzQK9x9IhVxCITrwu1pT7yVl0tq2ruogAFKECB6gKOh8LDw8Or7+AnCgSIABdOATLRTJMCFKCAHgLiofAJEybo0RX7oIApBVjHyZTTxqApQAEK+F6grKwM+/fvx9133+37wTkiBQwiwCtOBpkIhkEBClDA6AI//vgjZs2aBX4vndFnivF5U4ALJ2/qsm8KUIACFhEQlcKLi4sN/Zt0FqFmGgYX4MLJ4BPE8ChAAQoYQWDTpk1o1qwZunfvboRwGAMF/CbAOk5+oGcdJ++gs46Td1xFr6yJQ1txDpw6dQp//etfvYehY888Z3XEdOmKdZwsVV3BHMmwjpP7POlRX4R1nNxdxRY1W9Zx0uam5ipjL9qo1cTRY5z69iFqNom/t3r06OEZq3JrfcdxdK7Wj9p+GVfRRq0ftf0yfci0UTsHZPqQaaNXPjLxinis+jLRrTobyvLXYX5cV4grNkFBQ5CQmoVim8tS2P7xFDISelW2E23DMGTJQTg3tRVnITVhiL1NWNwiZBVfdO/IVoyc1AQMEOOFxWFBVnG1PtwP4BYKUIAC1hNYv349xo8fj6uu4i9iW292mVFdBUyzcLIdX4t3/w0MW7QHivIzinYMww+JwzEmOQtlLlnbjn+JD9/PcdraD6P7tUNVsmVZSB7zCvKGLEGF8jNy4k4hYcwi5JQ5L61OIyd5AqbkDcayCgUVOU/gZMIEJOecduqXbylAAQpYW6C8vBxLly7FU089Ze1EmR0FJAWq1hKS7f3U7AKOfNscj74wBOEhIuSGCI0ahxdf7YdNyauRdbb6gif3o3S0/OAkFEWp/G8FxoY3qoz9AvJXzEdy1GRMG9gawaKvgc9hRtSnmL4iv+qKki0/DdOTO2PGtEEIDQaCQwdh2ozOSJ6ehnzn4fwkwmEpQAEK+EJg165d9i/07dGjhy+G4xgUMLyASRZOjdChfx+0rhZtQ9zUriNCXYnP7sKK5KWYNzMJS9I2Ib/aVSQAtqPIXL4LXSPCEFJ1bHP0GvIb7Fv+FQrsi6ILKMhci/VdO6KNfaEmGgajSa/BeHLfWmQWXKg6km8oQAEKWFlg8+bNWLhwIWs3WXmSmVudBKotRep0pEEaXzu0FyKqFjcXkP/pO5hXDGDTPIwbOQARD72EtPyzVdHaCr7C8vVN0b1dyyu37hx711cuiuyLq0yEdm+Hm9yEMrE882jVlSnHofxJAQpQwGoConbTiy++iH79+lktNeZDAc0CbssCzT35/MBSZK87jmcmDHS6EtUI4WNXXH4GKvtfSJkaDWyag5FPp1Q+v2RDWWEB9qE9Itpcud7kFnpZEfL2weWqlFsrbqAABShgaYHs7GxERkaydpOlZ5nJ1VXApHWcbCjLeRPPfdEHi6ZEOd1yc03/Iooz5mDMoH8hauNazB3YHGczXkKnQQV4NW+p03NPturbb/oKCZ2ewO5XM7BmbKcrV6bOZnje7josgN69e3vYenlTVlYWoqKiatzPHRSgAAWMIHDkyBFce+21uPHGG40QDmMwkMCOHTsMFI2PQzFlnYVzO5TkqUuVA+cqJMI/qWyc2lMJnbpROaMoSkVeihKNnsrUjSedjq1QzmxMVEIxSknJK1eUigNKSnRo1TFVDc9sVKaGhirRKQcUmZGrjnN5wzpOLiAS9VTEEWo1SFjHyd1Vxo11nLS5qZ2PMvaijVpNHD3G0dJHSUmJvXbTsWPHqoB8EauMm0w+arHqNY5MLGpt9IjVl/nIxFt10ljwjflu1dm+Q/q7RzB0xuPoVPVsU22rzRC0iYiouu0W3PEujI6+xuWAi/jhaAGKo+9Dv46NgOB26Dfa/Z6+7Yej2F3sUtrApSd+pAAFKGAFgc8++wwxMTFo06aNFdJhDhTQTcBcCyfbcWS8vgbXP/bwlUVT2ddIXbIVVx7/drUpQ2FBVyQ8En75lpt9UdQa76/b63RMGQrzjiN69F3oaBdphI797kPX9zcgu6rUQeXzUY7Flesw/EwBClDAQgJpaWkYMWKEhTJiKhTQR8A8C6eyg0hLHItBk5/FoLBrrlQFvz4ay9Di8nNOotJ3+ufIcVQBtxUja0EyNg1+Ev2bOFJthPBHp2ByVjJeyzgOG8RzUIswM+sRzH60cnElig+Ej8DsyQcw87WN9urktuKNeG3mAUyePQLhjq70mQP2QgEKUMBQAoWFhUhPT8fAgQMNFReDoYARBMyxBLB9h7QXRmHkvPUezJxvndlwZsfr6GVfWHVFXPKXKHtgGl6xF7p0OjQkCpOXJaJV6n1oENQOY9a1x/xlz6FntVt/TdFz8luY2+oD9GwQhAZjNiBi/luY3LOpU0d8SwEKUMB6AhkZGbxNZ71pZUY6CZjji4eCb8GIlH1QUlSyDm6NgbPXQZmt0k5cUQrti0mp+zAptZa2waGImpSKolob1XI8d1GAAhQwoQBv05lw0hiyzwTMccXJZxwciAIUoEBgC/A2XWDPP7NXF+DCSd2ILShAAQoEjABv0wXMVDNRjQImLYCpMVuDHBYUFIRVq1YZJJraw5gzZw4SExNrb2SQvSdOnMD27dvtz2YYJKRawzCTLWOtdSrrtdNotiKePn36YMCAAW55GS1WtwCdNjBWJwyd3wpbFsC0YIEqI6fEApjus6NWIE4codaGBTDdXWXcWABTm5va+ShjL9qoFRPUYxzZPkSxS/H3k3PRS2cdX8Qq4yaTj1qseo0jE4taGz1i9WU+MvE6nzdWe89bdTqvxNkdBShAAbMK8DadWWeOcftSgAsnX2pzLApQgAIGFuBv0xl4chiaYQS4cDLMVDAQClCAAv4TKCkpYdFL//FzZBMJcOFkosliqBSgAAW8JfDtt9+y6KW3cNmvpQS4cLLUdDIZClCAAtoEcnJy+N102uh4VIAJcOEUYBPOdClAAQq4CpSWlmLDhg32MgSu+/iZAhSoLsA6TtU9fPKJdZy8w8w6Tt5xFb2yJo61bXfv3o0PP/wQSUlJtSbK86BWHs07zeQqkmQdJ6sVWDBBPqzj5D5JanVOxBFqbVjHyd1Vxo11nLS5qZ2PMvaijVpNHD3GUesjPj5e+f3vf+8ZwmmrL2KVcVPLR8ZVr3FkYlFro+YqE6tMG7U4ZPoQbWTiFe2s+uKtOs3/RuCBFKAABcwvUF5ebr/S1LlzZ/Mnwwwo4AMBLpx8gMwhKEABChhVYNeuXfbQbr31VqOGyLgoYCgBLpwMNR0MhgIUoIBvBTZv3oxZs2b5dlCORgETC3DhZOLJY+gUoAAF6iuwevVq/OY3v6lvNzyeAgEjwIVTwEw1E6UABShQXUD8Nt3OnTvB55uqu/ATBWoT4MKpNh3uowAFKGBhgb1792L8+PFo3ry5hbNkahTQV4ALJ3092RsFKEAB0wiIL/UdOnSoaeJloBQwggALYPphFlgA0zvoLIDpHVfRq5kK9JkpVn/anjt3DrGxsVi8eDFatGghdfKYyZaxSk2ppkbCdseOHZqOtcRBVi1QZeS8WADTfXb0KMzGApjurmKLmi0LYGpzU3OVsRdt1IoJ6jGOpz7WrVunREZGViXvqU3Vzso3vohVDKUWi9p+0YdarHqNIxOLWhs9YvVlPjLxinis+uKtOkssf5kEBShAgboJiO+mE1ec+KIABeomcFXdmrM1BShAAQqYXcBRLTw3N9fsqTB+CvhcgFecfE7OASlAAQr4VyAvL88eQEREhH8D4egUMKEAF04mnDSGTAEKUKA+ApmZmYiPj0fjxo3r0w2PpUBACnDhFJDTzqQpQIFAFhDPNw0ePDiQCZg7BTQLcOGkmY4HUoACFDCfQGFhIdLT03H77bebL3hGTAEDCHDhZIBJYAgUoAAFfCWwf/9+xMTEoE2bNr4akuNQwFICLIDph+lkAUzvoLMApndcRa8sJmgd29TUVLRq1Qr3339/nZPieVBnMqkDzOQqEmIBTKtWqDJwXiyA6T45agXixBFqbVgA091Vxo0FMLW5qZ2PMvaijVoxQT3Gce5D/P2TmZnplrRzG7edlRt8EasYSi0Wtf2iD7VY9RpHJha1NnrE6st8ZOIV8Vj1xVt1Uv8eYCMKUIAC5hfYvXu3PYkePXqYPxlmQAE/CXDh5Cd4DksBClDA1wJ79+7F+PHjWYbA1/Acz1ICXDhZajqZDAUoQIGaBdLS0jB06NCaG3APBSigKsCFkyoRG1CAAhQwv0Bpaam9DEGXLl3MnwwzoIAfBbhw8iM+h6YABSjgK4EDBw4gMjIS4eHhvhqS41DAkgJcOFlyWpkUBShAgeoCmzdvxvDhw6tv5CcKUKDOAqzjVGcyuQN69+5dY8OsrCxERUXVuJ87KEABCugt8M0339iLXt5www16d83+AlBgx44dAZh1ZcpWrbNg5LxYx8l9dtTqnIgj1NqwjpO7q4wb6zhpc1M7H2XsRRu1mjh6jLN48WJF/L1TUlLiOVmJP1++ilXGTcZEzVWvcWRiUWujR6y+zEcmXhGPVV+8VRe4a2ZmTgEKBIjAsWPH7F+z0rx58wDJmGlSwHsCXDh5z5Y9U4ACFDCEwJ49ezB48GBDxMIgKGB2AS6czD6DjJ8CFKCAisDq1atx5513qrTibgpQQEaACycZJbahAAUoYFKB/Px8e+T8mhWTTiDDNpwAF06GmxIGRAEKUEA/ga+//tp+m65x48b6dcqeKBDAAlw4BfDkM3UKUMD6AmvWrMHtt99u/USZIQV8JMCFk4+gOQwFKEABXwuUl5dj8eLFaNeuna+H5ngUsKwAC2D6YWqDgoKwatUqP4xc9yHnzJmDxMTEuh/ohyNOnDiB7du323/t2g/D13lIM9ky1jpPr/QB3rQ9cuQIJk+ejOXLl6Nhw4bSMdXU0Jux1jSm1u2MVauc+nHClgUwrVqlyqB5sQCm+8SoFYgTR6i1YQFMd1cZNxbA1Oamdj7K2Is2asUE6zNOamqqMn78eNU/O0aI1XkW1HJW2y/jKpOzzDh6tFE7B2RilWmjR6yytqKdVV+8Vae+uGYLClCAAqYU2LJlC4YOHWrK2Bk0BYwqwIWTUWeGcVGAAhSoh4Dj+aYuXbrUoxceSgEKuApw4eQqws8UoAAFLCCQl5dnzyI8PNwC2TAFChhHgAsn48wFI6EABSigm0BmZibi4+N1648dUYAClwW4cOKZQAEKUMCCAhs2bECfPn0smBlTooB/Bbhw8q8/R6cABSigu0BpaSnS09PB55t0p2WHFADrOPnhJGAdJ++gs46Td1xFr6yJYy7bgwcP2uuv6V0vjueBd84DM7k6/j5gHSerFlswaF6s4+Q+MXrUF2EdJ3dXsUXNlnWctLmpucrYizZqNXy0jLNw4UIlPj6+KjEtfVQd7PTGG7E6dV/1Vi1etf2iI7VYRRu1ftT2y/Qh00aPWGXG0SsfmXhFPFZ98Vadd/4BwV4pQAEK+E2Azzf5jZ4DB4AAF04BMMlMkQIUCBwBPt8UOHPNTP0jwIWTf9w5KgUoQAGvCBw4cMDeL+s3eYWXnVIAXDjxJKAABShgIYHc3FzWb7LQfDIV4wlw4WS8OWFEFKAABTQL8PkmzXQ8kAJSAlw4STGxEQUoQAHjC/D5JuPPESM0vwAXTuafQ2ZAAQpQwC7A55t4IlDA+wIsgOl9Y7cRWADTjUSXDSyAqQujx07MVKDPTLEKbD3j/fzzz3Hy5EnExcV5nMf6btQz1vrGonY8Y1UT0r5f2LIAplWrVBk0LxbAdJ8YPQqzsQCmu6vYombLApja3NRcZexFG7VignUZJyYmRlm5cqVbQnXpw+1gpw16xurUrdtbtXjV9osO1WIVbdT6Udsv04dMGz1ilRlHr3xk4hXxWPXFW3XaF908kgIUoIBhBPh8k2GmgoFYXIALJ4tPMNOjAAUCQ4DPNwXGPDNL/wtw4eT/OWAEFKAABeotwPpN9SZkBxSQEuDCSYqJjShAAQoYW4D1m4w9P4zOOgJcOFlnLpkJBSgQoALnzp1Deno6unTpEqACTJsCvhPgwsl31hyJAhSggFcEjh8/bu+X30/nFV52SoFqAlw4VePgBwpQgALmEzh8+DC/n85808aITSrAAph+mDgWwPQOOgtgesdV9Mpigsa2FfMzYMAA9OnTx3uB8jzwmq2Z/nw5/j5gAUyrVqkyaF4sgOk+MXoUZmMBTHdXsUXNlgUwtbmpucrYizZqxQTVxjl//rwi/k7Jy8vznIjEOeCrWGXHUctZbb+Mq0wsMuPo0UbtHJCJVaaNHrHK2op2Vn2Z6FadDWX56zA/rivEFZugoCFISM1Csc39HwG24iykJgyxtwuLW4Ss4otujWTawFaMnNQEDBDjhcVhQVYxPAzn1jc3UIACFPCVQF5enn0oPt/kK3GOE+gCplk42Y6vxbv/BoYt2gNF+RlFO4bhh8ThGJOchTLnWSzLQvKYV5A3ZAkqlJ+RE3cKCWMWIafMackj0wankZM8AVPyBmNZhYKKnCdwMmECknNOO4/G9xSgAAX8KrB3714MHz7crzFwcAoEkoBJFk4XcOTb5nj0hSEIDxEhN0Ro1Di8+Go/bEpejayzjkXRBeSvmI/kqMmYNrA1gkW7gc9hRtSnmL4iv/JqkUwbwJafhunJnTFj2iCEBgPBoYMwbUZnJE9PQ75juEA6U5grBShgSIEtW7YgIiLCkLExKApYUcAkC6dG6NC/D1pXi7YhbmrXEaHOs2I7iszlu9A1IgwhVdubo9eQ32Df8q9QIBY8Mm1wAQWZa7G+a0e0sS/URGfBaNJrMJ7ctxaZBReqeucbClCAAv4SKC8vx+LFi3HzzTf7KwSOS4GAE6i2FDFj9tcO7YWIysWNreArLF/fFN3btYRbYusvL3hk2lxeXGUitHs73OTWUSaWZx7ls05mPFkYMwUsJuB4viksLMximTEdChhXwG1ZYNxQXSMrRfa643hmwsDKK1E2lBUWYB/aI6LNletN1Y+SaQOgrAh5++By5ap6T/xEAQpQwN8C4vmm+Ph4f4fB8SkQUAImreNkQ1nOm3juiz5YNCWq8racDWczXkKnQQV4NW8pxoY3qpxI5+3v4ZHCV1XaLMXYm75CQqcnsPvVDKwZ2+nK1auzGZ63ezhlevfu7WHr5U1ZWVmIioqqcT93UIACFJAROHLkCJo2bYpmzZrJNGcbCugmwDpOZiu2cG6Hkjx1qXLgXEW1yCvyUpRo9FSmbjzptL1CObMxUQnFKCUlr1yRaaNUHFBSokOV0KkblTNOPSlnNipTQ0OV6JQDSvWRnRupv2cdJ3cjPeqLsI6Tu6vYombLOk7a3NRcZexFG7UaPjWN41y/qaY2jszU9ns7VkccsuOoxau2X4yj5ioTi8w4erTRI1Zf5iMTr4jHqi/z3aqzfYf0d49g6IzH0anqwe3Li+jgjndhdPQ1Livqi/jhaAGKo+9Dv46NINMGwe3Qb3Q/l34A2w9Hsbu4H0b3a3flKpRbK26gAAUo4H0Bx/NNrN/kfWuOQAFnAXMtnGzHkfH6Glz/2MNXFk1lXyN1yVacFVnZFzyt8f66vZc/2zMtQ2HecUSPvgsdRbYybdAIHfvdh67vb0B2VamDyuejKhdgzoh8TwEKUMDXAny+ydfiHI8ClwU0LpwUXPrpJ1wQhf599So7iLTEsRg0+VkMCrumsnp4EIKuj8YytKh8zqkRwh+dgslZyXgt4zhsuIjijEWYmfUIZj8aXnmVSKYNEBw+ArMnH8DM1zbaq5PbijfitZkHMHn2CIRrVPMVFcehAAWsLyDqN3n7u+msr8gMKVB3AY1LgJ+w5+2H0OWhyXhjeQb2HDuLS3UfW/4I23dIe2EURs5b7+EYl1tnIVGYvCwRrVLvQ4Ogdhizrj3mL3sOPZ1v68m0QVP0nPwW5rb6AD0bBKHBmA2ImP8WJvds6iEGbqIABSjgOwFH/aYuXbr4blCORAEK2AWu0uZwNVp16oOb31mIFx5bAOA2DHg6Dk88OBj9+/VA+6ZXa+u2pqOCb8GIlH1QUmpqUH17cGhfTErdh0mp1bc7f5Jpg+BQRE1KRVFtHTl3yvcUoAAFfCDA55t8gMwhKFCDgMYrTtfg5gdnY+PXh5H31Uq8MbUHzn74EsY91Acd2vbFowkLkbYtH6cu8LtJanDnZgpQgAKaBfh8k2Y6HkiBegtoXDhdHjeoUSuE/3oEJs79CNuLv0P2Zyl49fFm2DXveYy8KwKtugzFs/NXYvv3ZfDl41D1VmEHFKAABQwswOebDDw5DM3yAvoUwLx0Fse+ycZXm9dh5dL38UlOMRByJ/r3KMOmL78FQobiT6v/DzMGtYHGe4OWmoigoCCsWrXKFDnNmTMHiYmJpoj1xIkT2L59O2JiYkwRr5lsGav3Tqm62l68eBGjR4/GokWL4OuvWqlrrN5TU++ZsaobaW0hbFkAU0uVKlu5cjJvm/Kvd6Yro3qGigtKChCqRMa+oqT8a7ty6MeLiiLafPOpMjWymYJ+byvfXNIykPWOYQFM9znVo4gcC2C6u4otarYsgKnNTc1Vxl60USsm6DpObm6u/e9b56hd2zjvk41DrQ8tsbrGoVcsesQqE4vMOHq0UTsHZGKVaaNHrGIcmXhFO6u+NF4A+gl7Fj6C7i+sBRCCDgOeRNJHj+Devr1wR9smTleVrkbLzj3Ro/0NCPn5OjQK0rq+5XEUoAAFKCAE+HwTzwMK+FdA48IJCArpiqmvx2JA19sQEXknbg1pAOAnHM3ZgfNhXdE59FrY10lBbfDAot042fwGLpz8O9ccnQIUsICAeL5p6NChFsiEKVDAnAIaHw6/Dr/63YuIbbYNfxr2DN7J+vFy9hVHsPaPQ3FH+CP488bCytpOVyGkBRdN5jw9GDUFKGAkAdZvMtJsMJZAFdC4cKpA6Rfz8UjsP3D6gUcxoF3jy37BN2PI7L9hauTXeGV4Apbmnw9UV+ZNAQpQQHcB1m/SnZQdUqDOAhoXTj9i97o1ONjsSbyWPAn3tb/u8sBBTXDr3U9i5oJ43FX2BZZnfg9WcqrznPAAClCAAh4F+HyTRxZupIBPBTQunMpx+ofTQPP2uOV/XKuEB6Hh/7RGRxTjUOlPXDj5dDo5GAUoYGUB1m+y8uwyN7MIaFw43YBburYHDm3DzvyfXHKtQOne7fgPbsPd7VtBPDLOFwUoQAEK1E+AzzfVz49HU0AvAY0FMBX8kv8PjOo5Dhs7j8WfJj+Gu29rjquVn1Cc82+8k/QW/n31H7Fx658xsDmXTq6TxQKYriL6fGYBTH0cPfXCYoKeVPTZJmt78OBBezFafxbPlY1VH5n69cJY6+dX29HClgUwNVWpuqAUbV6gjL4tpLL4pf1bVezvQ/rHKx9/c1qxaerX+gexAKb7HOtRmI0FMN1dxRY1WxbA1Oam5ipjL9qoFRN0jLNw4UIlPj7eY7CONh53SpwDesdaUxyy4+iRj5qrTCxqccj0IdNGj1hlxtErH5l4RTxWfWmu4wRcg9B7/oiP9o7Gn/YcwOHjp3Ex+Dq0urUjOkfcipaNNN4FrG2Zy30UoAAFAlRgw4YNiI2NDdDsmTYFjCNQj4XT5SSCGoXi9t6huN04OTESClCAApYSKC0tRXp6OubNm2epvJgMBcwoUL+F06UyFB8+jKJzv3jIvQGuv6Uzwlte42EfN1GAAhSggKzAgQMHEBkZifDwcNlD2I4CFPCSgOaFk1K2F/+Y+BTGvZdbQ2gdELvyC6SOaFvDfm6mAAUoQAEZgdzcXAwfhsITKAAAIABJREFUPlymKdtQgAJeFtC4cCrD3iXTMe69HxAZ+wqevv92NLva9Rt8r0arO5t7OXx2TwEKUMD6AuL5pgkTJlg/UWZIARMIaFw4/YhDOQeB0Ccwc8F0DGHJARNMNUOkAAXMKFBSUmJ/vunNN980Y/iMmQKWE9BYx+kUMhLuw6CPHsSXB17G3de5Xm2ynJOuCbGOk66cVZ2xjlMVhe5vWBNHd9KqDtVsd+/ejQ8//BBJSUlVx/jrjVqs/orL07iM1ZOKPtuELes41bnYgk0p//rvyrCQXyt/XFWglLNgU50EWcfJnUuP+iKs4+TuKrao2bKOkzY3NVcZe9FGrSbO448/rsyaNctzkJVb1WJR269XrHqNo9aP2n4ZV5mcZcbRo43aOSATq0wbPWKVtRXtrPrSeKvuZ3z/9X6cvXEf/vZwRyzu+QCG39EC1Ss3XYuu41/BlLtb6bPEZS8UoAAFAlBA/Mv+2WefDcDMmTIFjCmgceFUgfITedh0qMyeVVnOv/FBjmuCnfD0KE9lClzb8TMFKEABCngSEPWbCgoKcMstt3jazW0UoIAfBDQunK5Dt+fXQHneDxFzSApQgAIBIiDqN4lXmzZtAiRjpkkB4wtoXDhVJqacR/GuTVjzxZfI2ncGHce/gkk37cT/7QvDI8O6odVVfGjc+KcAI6QABYwqcOjQIdZvMurkMK6AFaj+WFJdGJRT2P7Xp3B3rwcwLn4u/r70P9h38iecOZyBF0cOw+iZG1B8SXznL18UoAAFKKBFYMuWLYiIiNByKI+hAAW8JKBx4VSB0i9ex+/id+KOpE34bvMcdLAH2ADNB72AjxI64ItXZmNJ9hkvhc1uKUABClhfYPHixbjxxhutnygzpICJBDQunH7E7nVrcLBZDH4f2xdh1znd8buqLe4d+ySisQdrdxeiwkQYDJUCFKCAUQTy8/PtobRu3dooITEOClAAgMYCmMeQFjcAI7c+g+yDU9Btz3x06vUO+jq+m644DXFhI7E1KRsHp/SE07KK6AI9KAirVq0yhYWZisixAKb3TikznQdmilXMWE3xisKXa9asQWJiovcmto491xRrHbvxSXPG6j1mYcsCmHWuUvWjsu3V/gpCxioff/ez8kt2ktIBHZTYld8rinJJKVkbr4TiNuWpld8prI3pjssCmO4mehRmYwFMd1exRc2WBTC1uam5ytiLNjUVPxRFL8V/eoyjRx+1xeoQ1GsctX7U9svEKtqo9aO2X6YPmTY1nQPiWMdLj1j06EPEIxOvI24r/tR4q+4GdB/+WwzDCsx4+T1sO1qKClSg/Mej2LNuESZNfBvFtz2Ikb8OBX+vznurfvZMAQpYVyArKwu9evWyboLMjAImFdB4Fy0Ije6Iwzur/4vHhz+Ne967nP3R8ffgE/H2tscxPzUBD4RebVIWhk0BClDAfwKi8GV6ejrmzZuH/fv3+y8QjkwBCrgJaFw4iX6uQeig6fg8fxi2bcvGvsOluIgQ3BjRBb3v7o3wplw0uWlzAwUoQAEJge+//97eKjw8nAsnCS82oYAvBTQunCpQduwA8v77sz3WJrd0Q1+nbwQ4d2gvctAA19/SGeEtr/FlPhyLAhSggOkFDh8+jPj4eNPnwQQoYEUBjQuncuQtn4he8ZtqMemAWMdv2dXSirsoQAEKUKC6wPbt29GlS5fqG/mJAhQwhIDGhVMj3HJvIlaunOiSxEWcPrwdae+k4b+DX0Dsnc1d9vMjBShAAQqoCSQlJSEzM1OtGfdTgAJ+ENC4cLoKLbtFY0Q3TxGPwvCuDdHlt7koiufv1HkS4jYKUIACNQkUFhbad3Xu3LmmJtxOAQr4UUBjAUyViO0FMMfj8NtfYtMzXdBApbkVd/fu3bvGtMSvGUdFRdW4nzsoQIHAFThz5gzE4umOO+4IXARmbngBFsDUtULVz8qJtYlKJzRT+r29T7mka9/W6IwFMN3nUY/CbCyA6e4qtqjZsgCmNjc1Vxl70ca1mODChQvthS8dUekxjh59eIrVEaPjp17jqPWjtl8mVtFGrR+1/TJ9yLRxPQfEMa4vPWLRow8Rl0y8rvFb6bPGW3UXkL/8z5j1ebH7qrj8e2z9ZBMOhQzH67++OSCvNrmjcAsFKEABOYE9e/Zg6NChco3ZigIU8LmAxoVTBcpP7MHSpWs9BByKnsP+iDf+dwqe7dbEw35uogAFKEABTwLl5eVYvHgxSxF4wuE2ChhEQOPC6Tp0e34NlOcNkgXDoAAFKGABgWPHjtmzaNu2rQWyYQoUsKaAxu+qsyYGs6IABSjgT4Gvv/4a48ePR+PGjf0ZBsemAAVqEdB4xal65fBa+r+y6/pb0C28JTQOeKUfvqMABShgUQFR+LJbN491XiyaMdOigPkENK5jZCqHu2DErkRR6giEumzmRwpQgAIUuCywadMmLFiwgBwUoICBBTTWcbqEU3tWIGnSNMzb2Raxk8ZgcLdQXIefcGLPBvxjwVIciJyKvz3XG80qa2AGt7oT9919KxoZGMNXoQUFBWHVqlW+Gq5e48yZMweJiYn16sNXB584cQLiX+wxMTG+GrJe45jJlrHWa6prPdhhe+7cOcTGxtofDm/RokWtx/hrpyNWf41fl3EZa1206tZW2LKOU50LLPyinFiboHRCfyVh7ffKL9WOL1e++/hppRnuVV7dVlJtDz9cFmAdJ/czQY/6Iqzj5O4qtqjZso6TNjc1Vxl70cZREyczM1Px9HeDHuPo0YdzrJ7F1M81WRO1eNX2y8QqE4vMOHq0cZwDNbnKxCrTRo9YxTgy8daWi9n3aXw4/L/IWpWOg+3uxfD+bVyeW2qEm++JxkP4D/6ReQSX6raQZWsKUIACASlw6NAhliEIyJln0mYT0LhwaoCrG10DnClEUYnr0qgCZwu+wS6EokPz66BxALM5Ml4KUIAC9RLYsmUL+vTpU68+eDAFKOB9AY3rmpaIHPYQOv34PqZNno+VW77GkeJiFB/LR87av2Pq/76Nr297DBOHduDCyftzyBEoQAELCIjCl+3bt7dAJkyBAtYW0PhbdQ3QfMAUfJpyAg+Pm45Hlk+vphQSORFLV72MB0KvrradHyhAAQpQwF0gPz/fvjEiIsJ9J7dQgAKGEtC4cAIQdAPuGLsIWf3HYUf2N8j7vhQXGzbHzRF3oFfvHmjflIsmQ800g6EABQwrIApfit8GZeFLw04RA6NAlYDGW3WVxyu/oPzHEhz/Ph/79x0C7nwII9uXYF3GNzh5SfyCCF8UoAAFKKAmcPDgQQwePFitGfdTgAIGENC+cFJOYftfn8LdvR7AuPi5+PvS/2DfyZ9w5nAGXhw5DKNnbkAxF08GmGKGQAEKGF1g9erVCA8PN3qYjI8CFBA33EQ9hbpLVKA048/oO+gDhCe9h4VR2zDwN4vRd+UXSB0GrHspFvfNBV7dtgov9mla9+4tfgQLYHpnglkA0zuuolcWE/Se7cyZM7Fr1y5DF750ZM/zwCGh708zuYrMWQBTUyWqk8rGqT0VNHtB+deJX5RfspOUDuigxK783t5bRV6KEo1mSr+39ymXNPVv7YM8FblzzVitUJnaftGfWpuSkhJl69atrkNX+yxT6EyPcdT6kMmHBTCrTV3VBzVbFsCsoqr2Rs1Nbb/oTKbN7bff7rHwpSMYmT7U2qjtl41V7e8DvcZR60dtv8hHLVaZnGXG0aONHrH6Mh+ZeEU8Vn1pvFVXjtM/nAaat0Foc/fny4Ovb4qb8COKy36GhstZ+i7l2RsFKEABAwtcuHCBhS8NPD8MjQKuAhoXTtcjLLwtcOIACoouuvRZgdK92/Ef3Ia727dCA5e9/EgBClCAAlcExHfUsfDlFQ++o4DRBTQunG5A9+G/xTCswIyX38O2o6WoQAXKfzyKPesWYdLEt1F824MY+etQVH7Hr9EdGB8FKEABvwicPHmShS/9Is9BKaBNwP0+m1Q/QWh0RxzeWf1fPD78adzz3uWDjo6/B5+It7c9jvmpCSyAKWXJRhSgQKAKsPBloM488zazgMaFk0j5GoQOmo7P84dh27Zs7DtciosIwY0RXdD77t4IZwFMM58XjJ0CFPCBgCh82axZMxa+9IE1h6CAXgIaF04/4/CHCZh+sDcS//dRDBjxKwzQKyL2QwEKUCBABEThyyZNmgRItkyTAtYQ0FjH6RjS4gZg5Jdjse1gIvpcwyeZ6nI6sI5TXbTk27KOk7xVXVuaqc6MmWKNj49Hw4YNMWvWrLpOiV/am8mWsXrvFBG2O3bs8N4ARu9ZW52Fn5RDHz+r3BYySnl9W5FSbtPWS6AexTpO7jOvRy0U1nFydxVb1GxZx0mbm5qrmv2xY8fs9Zu6d+/uOYDKrfUdRy0Ox+Ay46jV75HpQ482Mn2oxSrjIjOOHm30iNWX+cjE6zivrPhT4626Bri65c3oHvo+Xvj1J3ix5wMYfkcLVP8VvWvRdfwrmHJ3K6OvHRkfBShAAZ8LfPfdd4iMjIS4As0XBShgHgH5hZNSgvysI7gQ1gld2wah9JvN+OTbMnumZTn/xgc5rkl3wtOjfnHdyM8UoAAFKAAgNzcX/fv3x+bNm+lBAQqYSKD6RaLaAj+1DcmDIzFieR4q0ACNb+yG2KcW4MvSSxBfd+f+3wG882BYbT1yHwUoQIGAFdiwYQMLXwbs7DNxMwvIX3G6dBHlZcD5QwUoKG6K777ZgqXvtcdv/liMjhc81QdvgMbNWqJpI/m1mZkhGTsFKEABWYHy8nKkp6dj3rx5soewHQUoYBAB+YXTjT0QM/ZOLH3nMXR+xxH9VxjX/QPHB5efHRC78gukjmjrsp0fKUABCgS2QF5enh0gPDw8sCGYPQVMKCC/cApuh4dfX4bPotbgwLnzKNz0D7z+7/9B7Izh6NrE01Wlhmjb4XoTkjBkClCAAt4V2Lt3L7/Y17vE7J0CXhOQXzgBCArphAee7oQH8BP2NMzE65tvw6iJ/4sHW3m6Vee1mNkxBShAAVMLiIrhXbp0MXUODJ4CgSqgsQBmoHLpkzcLYOrj6NoLC2C6iuj3mcUE9bMUPT388MNITk7GrbfeCtrqa+voja4OCf1/sgCmFatTGTwnFsB0nyA9isixAKa7q9iiZssCmNrc1Fxrss/Ly7MXvjx//rx9YLViglrHcc5Kjz5Ef76ItSa3uuajFqte4+hhq0esvsxHJl7n+bLae08PJ+m/PNWzx7J8ZKQtw/y4IUjIOFVDzzaczZiOsKAge3E5cYUnaMgS5NucmtuKkZOagAFiX1gcFmQVw3n35ZYXUZzzPhIGhCEoqCviFmxFsXsjp075lgIUoEDtAuI2XUxMDL/Yt3Ym7qWAYQXMtXCyHcSSx15C6so5iF9aUjOq7Rg2fPgvFFe1CEX06LvQsSrb08hJnoApeYOxrEJBRc4TOJkwAck5p6uOAGwoy1mEMVMOY8iyo1Aq1iLu5ByMSc7C5bKfTk35lgIUoICkgPhi38GDB0u2ZjMKUMBoAlVLCaMF5jGe4E4Y+9kK/OPlSYj22EBstKEsNw1/b/k6zlQV5izCurGdqr4SxpafhunJnTFj2iCEBgPBoYMwbUZnJE9Pu3JVypaPFdM/RdSM5zAwtCEQ3BoDp01GVPJ8rMi/UOPo3EEBClCgNoHVq1fjzjvvrK0J91GAAgYWqN/CSTmP4pzPsWT+NDwT9yzmbzmJim8/x9tpu3HykriN749XKbJWfIj18+Zi1pI0ZOSfdQniAgoy12J9145oE+JIPxhNeg3Gk/vWIrPg8qLIVvAVlq9vjYg2IVeOb/IrDHnyOJZnHvVwW+9KM76jAAUo4EmgsLAQO3fuxC233OJpN7dRgAImEHCsHOoeqnIK2//6FO7u9QDGxc/F35f+B/tO/oQzhzPw4shhGD1zA4r9sHiy5f8Tc+eJL85bj3njRmJQxCgkpB28cnvNdhSZyzMR2r0dbnLLPrNyUVS5uArtiHY3NXSx+Rnrl3+FAj7r5OLCjxSggJrA/v377V/s26ZNG7Wm3E8BChhUwG3pIBdnBUq/eB2/i9+JO5I24bvNc9DBfmADNB/0Aj5K6IAvXpmNJdln5LrTsVVw+FisUxRUFGVjdcpU9BcLqJFT8I7j+aWyIuTtA7pGhMHpWpJLBGUozDsMVLsq5dKEHylAAQrUUSA7OxvDhw+v41FsTgEKGElA48LpR+xetwYHm8Xg97F9EXadUx3Nq9ri3rFPIhp7sHZ3ISr8lG1waE/EjJ2LjUXrkdh/F5JX7ILrTTs/hcZhKUCBABXIyspCr169AjR7pk0BawhoLIB5DGlxAzBy6zPIPjgF3fbMR6de76Cv47vpitMQFzYSW5OycXBKTzgtq3RRs+UvwdCIt9B941rMHdhSpU9RmuAldHoC+ODgqxgYko8lQwfipe4f4ODcgWjiOPpsBhI6PYHdr2Zgzdh2KFgSi4iXOmKjOKbqK2VOISPhPgzaPQF5a8YivJZlZ+/evR09u/0Uf3lGRUW5becGClDAugKXLl3Crl270L17dzRs6PoIgHXzZmbWFNixY4c1E5PJSlthqh+Vba/2VxAyVvn4u5+VX7KTlA7ooMSu/F5RlEtKydp4JRS3KU+t/E6xaRug1qMq8lKUaPRUpm48WWs7x057++gUJa9CbClX8lJGKaFTNypnHA0URbnc5yglJa/cvtX+OTRR2XjGftDllhUHlJToDkp0ygHFaatTL3JvWQDT3UmPInIsgOnuKrao2bIApjY3NVdX+8zMTCUyMtJtMLVignUdx20AiXPANVZPfYhtvohVJhYZE7VY9RpHJha1NnrE6st8ZOIV8Vj1Vcs1k9qWXTeg+/DfYhhWYMbL72Hb0VJUoALlPx7FnnWLMGni2yi+7UGM/HUogmrrxif7bCgr/C96JgyrvELUCB373Yeu729A9lnHE96iTQH2Rd+Hfh0b2aMK7ngXRnfdjHXZpVeitD8f1QOj+7WrKm1wZSffUYACFKhZIDc3F/3796+5AfdQgAKmENC4cApCozvi8M7qBLT59Gnc88gcHMVRfDL+HnS/7wUsRQzmpybggdCrfYwgKn1/jvQcRxXwiyjO+j/M2tQTE/tfuaUXHD4CsycfwMzXNtorgduKN+K1mQcwefaIK7ffgsPx6OxHkDVzETKKLwK248h4LRlZk6fg0fDLiysfJ8fhKEABEwts2LABffr0MXEGDJ0CFBACGhdO4tBrEDpoOj7P34OMlSl4PSkJSUlvY+k/tyAv6x/431/f6IWrTeIZo15oEDEO65GDeYNauX+Vypmd+FuvMDQICkJY3BvYWjYQM165117o8sqUN0XPyW9hbqsP0LNBEBqM2YCI+W9hcs+mV5ogGCE9n8OyuS2R2vMaBDUYi3URf8KyyVG1/Dae0+F8SwEKUKBSoLS0FOnp6ejSpQtNKEABkwtofG77Ekry96OkeThuC/0VBoz4FQb4BKIlBs7NhjK3psEaInTgy/hCebmmBle2B4cialIqiialXtnm9q4hQqOeQ2rRc6itldth3EABClDASeDAgQP2T+Hh4U5b+ZYCFDCjgMYrThdw9J8vIKLVrzDo2fn4OGMPjpVdMmP+jJkCFKCA1wXE803x8fFeH4cDUIAC3hfQuHBqhFvu/QOSnrkV378Tj98O6o6bQ+/CozP+D59tz8epC46Hrr2fAEegAAUoYHQBPt9k9BlifBSQF9BYx8kxgA0XThUg98t1WP3x+3jrk52Xv9qkwzD88flYPD7qQfQKvcbRmD8rBYKCgrBq1SpTeMyZMweJiYmmiPXEiRPYvn07YmJiTBGvmWwZq/ZT6uLFixg9ejQWLVqEsLAwt45o60aiywa66sLosRNhyzpOuhRb+EU5991OZVXS75SeIVBQVddJl84t1QnrOLlPp1qdE3GEWhvWcXJ3lXFjHSdtbmrno8M+NzdXfOO550F8VBtJNtYag6zcoVa/R69x1PpR2y/CVYtVtFHrR22/TB8ybfSIVWYcvfKRiVfEY9WXxofDqy9ClQsn8W3uFqxbvQKpby1HThkQEjkY93S4vnpDfqIABSgQYAJ79+7l800BNudM19oC2hdOynkU79uOLzd9hvffeBf/PiRWS3chNiEFfxk6GL/p1hYhV/m//KW1p4/ZUYACRhfYsmULhg4davQwGR8FKCApoHHh9BP2LHwE3V9YCyAUPUc9j3f+Ngz39uuB9k19XfRSMlM2owAFKOBjgXPnzmHx4sW84uRjdw5HAW8KaFw4AUEhXTH1jd9j+AMDENm+me5f5OvNpNk3BShAAV8IHD9+3D4M6zf5QptjUMA3AvILp4p8LP/jHKy9ZSySp0Si0XXB+GFzOt7JTsc7HmO9Fl3Hv4Ipd7fyuJcbKUABClhd4PDhw7zaZPVJZn4BJyC/cEI5Tmz9FJ/+MhLzxBf6ntiDpUvFrbqaXp3w9KhfatrJ7RSgAAUsL7Bnzx4kJCRYPk8mSIFAEpBfODXohud3ncPzlTqtnl8DxfEhkMSYKwUoQAEJAfH9dFlZWfx+OgkrNqGAmQQ0FsC8hFN7MvDlkWtx5319cWsjl9+eu3AEX67MQGGn4fhtzxZe+LJfMxG7x8oCmO4memxhAUw9FD33wWKCnl1q23rw4EGkpKQgKSmptmagba08mnfSVTOd6oEsgKmpQtU5JTupvwI8raws+sWtB9v3HyujAaVDUrbivtetecBtqK0YngNDrVCZ2n7Rj1qbkpISZevWrY4hPf6UKXSmxzhqfcjkwwKYHqdQ9TxgAUxtbmrn7MKFC5XHH3/cc+dOW9X+jKmNI7pSa6O2X6YP0cYXscrEIpOPWqx6jSMTi1obPWL1ZT4y8Yp4rPqSv1WHS/jvZ1PQ6aHX8WPVenQTRob9vepT9TftMPzGJtD4ZXjVu+InClCAAiYTEN9P1717d5NFzXApQAE1gTosnK7C/wz5AxZP+wnpRedR8s0X+HdOCPqP6o2bG7suj65FaK+HMPbh9lw4qc0A91OAApYTKCwsRHp6Oh566CHL5caEKBDoAnVYOAG4uiNGzHkXI/AT9rzxCP6ddxv+d9ECPNiqQaA7Mn8KUIACVQL79+9HZGQkWrRoUbWNbyhAAWsI1G3hVJXzdegmfqtuwlkcy9+LnO9tVXvsb5TzOJn3DYo6PIKxfVpW38dPFKAABSwukJ2djdjYWItnyfQoEJgCGhdOgPLjNvz1qbGI/+fBGuQ64el/DcPYGvZyMwUoQAGrCqxevRoLFizAyZMnrZoi86JAwAq4PpwkCXEB365agPh/nkFk7DS88vQAhKAt+j/9EmY8HY0OaIbIhAV4+b5Qyf7YjAIUoIA1BPLz87Fz50507tzZGgkxCwpQoJqAxoVTKfKz9gHNHsWfkmbipYTfYRAuoWHU4/jz28ux8o3BOJC2HjknL1UbjB8oQAEKWF3g66+/RkxMDJo3b271VJkfBQJSQGMBzGNIixuAkVufQfbBKej58xb8qfM9WPzbjTg4dyCuP/I+Hm7/IrA0A6ue7MgCmC6nFgtguoDo9JEFMHWC9NANiwl6QKlh06JFi3D77bdjwIABNbSovpm21T30+kRXvSTd+2EBTE0VqkqUL2f8WkGzF5R/nfhFUSoOKCnRoQpiliqHbYrCApi1o7IApruPWoE4cYRaGxbAdHeVcWMBTG1uns7H8+fPK+LPd25urr1TT21cR1MrJijTh1obtf0y54lo44tYZWKRyUctVr3GkYlFrY0esfoyH5l4RTxWfWm8VdcU3e4dgk4//v/27gUsiuvuH/gXTI0aYg1qXhdJYw0B0oZoRdFG0+AlENOmGIy1sVFSL0lqNIm+AqLm6v3yN62XvLYJVkxiYhpQ/0mjYEDNC60SiKamVfhTQypCbKLxQrzQsPN/zsDCsrswwzKzOzP7nefhYXfmzDm/8zkDHGZmf/M2Xkz/A/56pid+8JMoID8H2977EPk73kUebkHcTaFgogL32TrXUIAC1hQoKyuTOxYVFWXNDrJXFKCAt/kpg9F9xOPYvGYUzm3Zj2NfX4/BUxfg2SGlWPTzu3HPU2/gPyMfw+yE7/EyHQ8yClAgYAQKCwuRmpqKrl27Bkyf2VEKBJqA1+kIEPRf+PF/b8HHE0/jap9rcc01Y/BMzj6MPfQpvkAYBg0fhO+F8HxToB1Q7C8FAllAPGZl5syZgUzAvlPA8gLeT5xkmmsQEt4XIY1M1/S4BcMSb7E8GjtIAQpQwFXA8ZiVDRs2uG7iewpQwEIC6idO9eXY/vRyvH/BJUt4qxjdEDP9Rcy7q3erJbiBAhSggFUEHI9ZCQ8Pt0qX2A8KUMCDgPqJEy7jdNE72Hq41kM1nlZF47EJ//G0gesoQAEKWE5AXKbjY1YsN6zsEAXcBLzM4+RWD1e0Q4B5nNqB1Y6izOPUDqx2FmVOnLbB6urqMHHiRAin6Ojotgu7bKWtC4hGb+mqEaSHaoTtoUOHPGwJkFVWzbNg5H4xj5P76CjlORF7KJVhHid3VzVuzOPknZvz8SjyNomfa5HHyXlxLuO83vm1Uk4cNXUolVHaLuJRU8YXsaqJRYtYtWpHTSxKZZRc1cSqpoxSHGrqEGXUxCvKWXVpx6U655lkPWpPHkPZv686r3R53QnX33wbIntd67KebylAAQpYS4BpCKw1nuwNBdoS8HLidBll22djcOr+Nuq+BVOy9yEr+aY2ynATBShAAfMLMA2B+ceQPaCAWgEvJ05dcPM9GcjOnu3STh3OnTiInE05+PeYpzDlR3zIpQsQ31KAAhYTYBoCiw0ou0MBBQEvJ07XoNeABCQP8FT7BIyL6YzbHzqM6tQgTwW4jgIUoIBlBEQagqSkJDANgWWGlB2hQJsCXj6rrq06OyH0jmG45+ud+MPeE6hvqyi3UYACFDC5wJ/+9CeMGTPG5L1g+BSggFoBL884tVV9Hf79txIUA+jVVjEeruEWAAAgAElEQVRuowAFKGBygcuXL+PVV1/F4cOHTd4Thk8BCqgV8HLidAXl25/H0vdr3Nu5/C8U/Wk//hkyDr/78ffAp9W5E3ENBShgDYGPP/4YQ4YMwcCBA63RIfaCAhRQFPAyAeY3+GTdgxj41B4PDdgQ+/OJSPnvefjNT/rCy5mZh3rNtWro0KGtBlxcXIy4uLhWt3MDBShgDoHq6mo50LCwMHMEzCgpoJEAE2BaNUuVQfvFBJjuA6NFYjYmwHR3FWuUbJkA0zs34Sp+lgsLCz1XoMJe7KiUTFBp/NSMsRZ1+CpWrfqj5KpVO1rYahGrL/ujJl4Rj1WXDp8Qkq6cw+mvL0P8Bmm5dELXG3qhRxcd7j9v2RDfUYACFPC5wGeffSa3OWjQIJ+3zQYpQAH/CXg9q5Fqj2Pn0ocxpPcNsIWFQZyqbvl1J556/5T/esaWKUABCugocOzYMUyfPh1du3bVsRVWTQEKGE3AyzNOV/HZjqWYvGgX/iv+ITx11x0I7+5aVWfcdMv1Rusv46EABSigicC+ffuwceNGTepiJRSggHkEXGc7KiP/N4588FfU2n6Dd7KXIzGUn51TCcdiFKCABQREtvCKigoMHjzYAr1hFyhAgfYIeHmprit69OkBXNMN3a71sor2RMmyFKAABQwkUFBQICe9DA3lY6UMNCwMhQI+EfBy1tMTdz2Wil93eR9v5BzFuW/dbw33SfRshAIUoIAfBHJychAbG+uHltkkBSjgbwEvJ05B+M7378HMR8PwxpQBuOE7wQgKCnL5ug2Pv9eQ48TfnWT7FKAABbQScDzU99Zbb9WqStZDAQqYSMDLBJj/Qc176bj7/pfw/2BD7E9H4oc9XW+X6oaY6S9i3l29TcThm1DFJHPHjh2+aayDrSxfvhwZGRkdrMU3u58+fRoHDx6UH7jqmxY71oqZbBlr81iLm8LFcabVzwVtm221fEVXLTVb1iVsmQCz3VmqTknvPhYt4YYZ0usVtZK93fsH9g5MgOk+/lokkWMCTHdXsUbJlgkw2+eWlJQkZWVlKbqqsRdllJIJKo2fmna0qMNXsWrVHyVXrdrRwlaLWH3ZHzXxinisunh5qa4zun33OuC7/XBLeDcEtZyM8h0FKEABSwo4LtONGjXKkv1jpyhAAWUBLydOPXHntDl45DsfYOcHlbjCe8OVpVmCAhQwvYD4NF1SUhLCw8NN3xd2gAIU8E7A9cYklbVcxb8OH8aX3Y9jy8+G4wPe46TSjcUoQAEzC4hP0yUnJ5u5C4ydAhTooICXE6d6XD79d/y5tEZuvvTP21DqFkg0HpvwH7e1XEEBClDAjAKOy3QbNmwwY/iMmQIU0EjAy4nTdRjw5G5IT2oUBauhAAUoYHABXqYz+AAxPAr4SMDLiVM9ak8eQ9m/r7YRZidcf/NtiOx1bRtluIkCFKCAOQR4mc4c48QoKaC3gJd5nGpRuuZ+DE7d30Z8t2BK9j5kJd/URpnA3MQ8TvqMO/M46eMqag30nDhnzpzB9OnT8eqrr6Jnz56aQge6raaYTpXR1QlD45fM4+RVooX/SF8eyZWys7Ndvt6UMlc/Jf30lpukIY+tkz44UetV7VbfiXmc3EdYi1wozOPk7irWKNkyj5Oym8jbJPI3OS9KrmrsRRmlnDhatKNFHb6KVY2bmv4ouWrVjppYlMpoEasv+6MmXhGPVRcvL9Vdg14DEpA8wNM0dgLGxXTG7Q8dRnUqMzx5EuI6ClDAXALiMt3MmTPNFTSjpQAFdBHwMo9TW7F0Qugdw3DP1zvxh70nUN9WUW6jAAUoYHCBI0eOYNeuXRg8eLDBI2V4FKCALwR0mDjV4d9/K0GxL6JnGxSgAAV0FigsLJTvbwoNDdW5JVZPAQqYQcDLS3VXUL79eSx9vyGPU4uOXv4Xiv60H/8MGYff/fh76NRiI99QgAIUMJfA1q1b8dJLL5kraEZLAQroJuDlxEkkwPwEW7fu8RCYDbE/fxrr/nsefjOgu4ftXEUBClDAHAJFRUX46KOPMGjQIHMEzCgpQAHdBbycODkSYNpx5atqfN3FBluIOLf0DSpLP8WlsBjcZuPDf3UfPTZAAQroKnDgwAEsXboUXbt21bUdVk4BCphHwPt7nKTz+PtrT+Mn3x+H3xZ/3dDj+s+w5+mx+GHkg3g+vwrfmseBkVKAAhRoIVBXV4eFCxfi7rvvbrGebyhAgcAW8DIBZj3OFjyP4aN/i/qJz2Ddsidwb//rAOkCPivciU3PLcKqj+5CZukrmBrZLbCFPfSeCTA9oGiwigkwNUBspYpATCYoPk33xhtvYPXq1a2oaLM6EG21kWu7Frq27dORrUyA6VWGqi+l/LRYCTf8Rso+VedSg126emSddCdsUkLmManeZSvfShITYLofBUoJ4sQeSmWYANPdVY0bE2B6dhszZoy0fv16zxtVHI9q7EUZpWSCSse9mna0qMNXsWrVHyVXrdrRwlaLWH3ZHzXxinisunh5qe4yzn1xDgjtj5tv/I7LxDUInW/siwjU4J9nv4HdZSvfUoACFDC6QFVVFT744AOMGzfO6KEyPgpQwMcCXk6cvoubY/oD//wrPir/xiXkepz920Hsxa24q39vpiNw0eFbClDA+AI7d+5EXFwcwsPDjR8sI6QABXwq4OWn6q7HHT//JZJemIbUR3rg4txf4q5bQ/Ed6RvUlP4Zm1b/D2qin8bk+L7gQ1d8Op5sjAIU0EBA5G667777NKiJVVCAAlYT8HLiFITvRP4K//PnC5gz/RmkPbS5hUtIfCre2jgPI0OZ/rIFDN9QgAKGF3Dkbpo3b57hY2WAFKCA7wW8nDiJQK+F7SdP482/TcSznxzDiVPnUBd8HXp/PwK3RX0fvbp4eRXQ9wZskQIUoECTgHguncjd1Llz56Z1fEEBClDAIdCBiVNDFUFdbPjBUBt+4KiR3ylAAQqYVODs2bNy+oHDhw+jsrLSpL1g2BSggJ4CPC2kpy7rpgAFTCXw3nvvISkpCQMHDjRV3AyWAhTwnYCXCTB9F6AVW2ICTH1GlQkw9XEVtQZKMsHU1FSMHz8ew4YN0w/TpeZAsXXptu5v6aofMRNgmi1D1cUyKT/7DWn1lAQpLf9Lz9HXV0slW9KkeECCbYq09lC1eyJONWWkq1J1yVYpLd4mAbdLU9YWStUaZPRkAkz3YdMiiRwTYLq7ijVKtkyA2eBWWFgoJ6c9c+aMvELJTWm7GntRRimZoBbtaFGHr2JV46amP0quWrWjJhalMlrE6sv+qIlXxGPVxVyX6uzHsfmXi5CVvRypW8+0Mp0+h9K1MzGvbAy21UuoL30YX6bPxNrSc07l1ZSxo7Z0IybNO4HEbZWQ6vcg5cvlmLS2GLVONfElBShgDQHHTeGhoaHW6BB7QQEK6CJgrolTcDSmvvc2/vjcHCS0wmEvz8GCtbfhmfmjYQsGgm2jMf+Z27B2QQ7KG9OYqykDezneXvAO4p55AqNsnYHgvhg1fy7i1q7B2+VXWmmdqylAATMKOG4KZ+4mM44eY6aAbwXMNXFStLmCisI9yIuJQHiIo2vB6D54DCYf3YPCCjHhUVMGsFf8Bdvz+iIqPKS51e53IHHyKWwvrOSjZJpV+IoCphfgTeGmH0J2gAI+E3DMLnzWoK4N2StRuL0QtoH90MetZ4UNEx41ZRyTK1sE+vVxzeVyFXnb/4IKPoRP16Fk5RTwlcDly5exYcMGzJw501dNsh0KUMDEAm7TCxP3BaitRtlRICYqDE7niVp2SU0Z1KKq7ATQ4sxVy2r4jgIUsIbA//7v/8odueuuu6zRIfaCAhTQVcBaEyddqVg5BShgRYGXX34Zs2bNQteuXa3YPfaJAhTQWMCUeZzs5ZsxNuplDMzfg5WjejWTiE/djR2FRQNfx/GVo9DdseVCAdKjH8aRJQXY/QiwRanM1H6o2DwFUYsikH98CUZ1d8wvv0JB+r0YfWQmynZPRaRjtaMdp+9Dhw51etfyZXFxsfzk9ZZr+Y4CFPC1QG1tLf7xj39g0KBBuOaaDj9Iwdfhsz0K+E3g0KFDfmvb7w2bMc9CfVmmlIBYD3mcLktlmRMkW1q+dN6pYw3lJ0iZZZclSVJTRpLkfWwZUv55p8RN9cekzIRbpITMY+55oZzaU3rJPE7uQkp5TsQeSmWYx8ndVY1bIOdxSkpKktavX+8RTul4U9quxl6UUcqJo0U7WtThq1jVuKnpj5KrVu2oiUWpjBax+rI/auIV8Vh1aeOcid/ndF4E0AURI+5FzGsfoOSC4+5tO2qrKnA04V6MiOgCQE0ZIDjiTkyMOYDckrPNccj3Rw3CxBH9YDG45j7yFQUCRODIkSMQuZsmTZoUID1mNylAAS0ELPf3PzgyGcvmHsPiFfmosQP2mnysWHwMc5clN11aU1MGwZH4xbIHUbx4Iwpq6gD7KRSsWIviufPwi0gxAeNCAQqYWWDbtm1YunQpmPDSzKPI2CngewGTTZzEPUaD0SlqGvJQilWjeyMocXNTYssGvh6InfsyVvZ+HbGdgtBp0geIWvMy5sb2cNJVUyYYIbFPYNvKXsiKvRZBnaYiN+pZbJsb1/on9pxa4EsKUMC4AtXV1Vi9ejUefPBB4wbJyChAAUMKmOxuyF4YtbIE0koFy2Ab4uZkoXpOVusF1ZRBZ9jinkBW9RNoo6bW2+AWClDAkAJ79+6FeKBvZGSkIeNjUBSggHEFTDZxMi4kI6MABcwhUF5ejp07d6KsrMwcATNKClDAUAImu1RnKDsGQwEKmFDg1Vdfxbhx43i2yYRjx5ApYAQBTpyMMAqMgQIU8ImAONsk7m265557fNIeG6EABawnYMoEmGYfhqCgIOzYscMU3Vi+fDkyMjJMEevp06dx8OBBJCUlmSJeM9laJdasrIa7FVNSUgxzjFjF1jCgjYHQVb8REbZMgGnVLFUG7RcTYLoPjFKCOLGHUhkmwHR3VeMWKAkwy8rKJPGzJ74rHUtq3LSoQ7SjlExQi3a0qMNXsWplr+SqVTta2GoRqy/7oyZeEY9VF16q029SzpopQAEDCYh7m/hJOgMNCEOhgEkF+Kk6kw4cw6YABdQLOO5t4ifp1JuxJAUo4FmAZ5w8u3AtBShgIQGebbLQYLIrFPCzAM84+XkA2DwFKKCvQFFRkfxJupMnT+rbEGunAAUCQoBnnAJimNlJCgSugEg/sH79eoSHhwcuAntOAQpoJsCJk2aUrIgCFDCagDjbtGvXLkyaNMlooTEeClDApALM4+SHgWMeJ33QmcdJH1dRqxlz4tTV1WHhwoUYOXIk7rvvPv1wOlizGW072GWf7E5X/ZiZx8mqiRYM3C/mcXIfHC1yoTCPk7urWKNka9U8TtnZ2dKQIUOkS5cuucEomahx06IO0Y5SThwt2tGiDl/FqpW9kqtW7Whhq0WsvuyPmnhFPFZdeKlOv0k5a6YABfwkcPnyZaxYsQLz589H165d/RQFm6UABawowImTFUeVfaJAgAtkZmYiLCwMY8eODXAJdp8CFNBagOkItBZlfRSggF8Fvv32W8yePRuFhYU82+TXkWDjFLCmAM84WXNc2SsKBKxATU0Npk+fjuHDhwesATtOAQroJ8CJk362rJkCFPCxgHi0ipg4iWfScaEABSighwAnTnqosk4KUMAvAuLRKjabDZGRkX5pn41SgALWF+DEyfpjzB5SICAEjhw5Ij9apXfv3gHRX3aSAhTwjwATYPrBnQkw9UFnAkx9XEWtZkgmKGIcMGAAPvnkE2RkZOiHoXHNZrB1dJmxOiS0/W4mV9FzEe+hQ4e0RTBTbVZNUGXkfjEBpvvoaJFEjgkw3V3FGiVbKyTAzM3NlcTP1ZkzZxQTSqoxUVNGyVVNHaKMUjJBLdrRog5fxarGTU1/lFy1akdNLEpltIjVl/1RE6+Ix6oLL9WZaZbLWClAATcBkexy0aJFyMrKQmhoqNt2rqAABSigpQAnTlpqsi4KUMDnArt375bbnDBhgs/bZoMUoEDgCTABZuCNOXtMAcsInD17FuPHj0dubi6TXVpmVNkRChhbgGecjD0+jI4CFGhDYNOmTUhKSkJCQkIbpbiJAhSggHYCPOOknSVrogAFfCggkl0uXLgQhw8f9mGrbIoCFAh0AZ5xCvQjgP2ngEkFVq9eLWcIHzhwoEl7wLApQAEzCvCMkxlHjTFTIMAFioqKILKEnzx5MsAl2H0KUMDXAkyA6WtxAEyAqQ86E2Dq4ypqNVKCvrq6OvkS3X333YeRI0e6ddpIsboF52GFmeJlrB4GUINVZnIV3RXxMgGmVbNUGbRfTIDpPjBKCeLEHkplmADT3VWNm9kSYD755JPSkCFDpEuXLnnssJrkfErHkho3LeoQ7SjFq0U7WtThq1i1sldy1aodLWy1iNWX/VETr4jHqgsv1Wnw3wKroAAFfCMg0g+sW7eO6Qd8w81WKEABDwK8OdwDCldRgALGFFixYgXGjBnD9APGHB5GRYGAEODEKSCGmZ2kgPkFjhw5AvFJugceeMD8nWEPKEAB0wpw4mTaoWPgFAgcAfE8uueffx7r169HWFhY4HScPaUABQwnwImT4YaEAVGAAq4C4nl01dXVmDZtmusmvqcABSjgUwHeHO5TbjZGAQq0V6CqqorPo2svGstTgAK6CTCPk060Q4cObbXm4uJixMXFtbqdGyhAgWYBkeTy22+/xfe///3mlXxFAQr4VYB5nKyabMGg/WIeJ/eB0SIXCvM4ubuKNUq2Rs7jVFhYKImfl5MnTzZ1Tqk/anLMKNWhxk2LOkQ7SvFq0Y4WdfgqVq3slVy1akcLWy1i9WV/1MQr4rHqwnuc/DpnZ+MUoEBrAuKG8Dlz5iArKwvh4eGtFeN6ClCAAj4V4MTJp9xsjAIUUCuQmZkpF50wYYLaXViOAhSggO4CvDlcd2I2QAEKtFegvLwcs2fPxuHDh9G1a9f27s7yFKAABXQT4Bkn3WhZMQUo4I2AuESXlpaGpUuXYuDAgd5UwX0oQAEK6CbAiZNutKyYAhTwRsCRs+nxxx/3ZnfuQwEKUEBXAV6q05WXlVOAAu0ROHPmDKZPny4/xDc0NLQ9u7IsBShAAZ8I8IyTT5jZCAUooEbgrbfeQmpqKh/iqwaLZShAAb8IMAGmH9iDgoKwY8cOP7Tc/iaXL1+OjIyM9u/ohz1Onz6NgwcPIikpyQ+tt79JM9n6IlYxditXrsSrr76Knj17th+0cQ9fxOp1cB52NFO8jNXDAGqwykyuorsiXibAtGqWKoP2iwkw3QdGiyRyTIDp7irWKNkaIQGmSHApfi7S09M9d8JprVJ/1CTnU6pDjZsWdYh2lOLVoh0t6vBVrFrZK7lq1Y4WtlrE6sv+qIlXxGPVhZfqNPhvgVVQgAIdE3jhhRfke5uGDRvWsYq4NwUoQAGdBXhzuM7ArJ4CFGhbICcnR748J55JV1JS0nZhbqUABSjgZwGecfLzALB5CgSyQFVVFcaPH4/s7Gw+ViWQDwT2nQImEuDEyUSDxVApYDUBxyW65ORkq3WN/aEABSwqwEt1Fh1YdosCRhdwvkRn9FgZHwUoQAGHAM84OST4nQIU8JmA4xJdbm4uL9H5TJ0NUYACWghw4qSFIuugAAXaJSAu0THRZbvIWJgCFDCIABNg+mEgmABTH3QmwNTHVdSqZYK+ffv24f3338ezzz6L66+/XvOgtYxV8+A8VGimeBmrhwHUYJWZXEV3RbxMgGnVLFUG7RcTYLoPjBZJ5JgA091VrFGy9WUCzI0bN8qJLgsLCz0GqxSrmv6oSc6nRTta1CH6oxSvFu1oUYevYlUzxmr6o+SqVTtqYlEqo0WsvuyPmnhFPFZdeKlOg/8WWAUFKKAscPnyZbz00ktYunQphg8frrwDS1CAAhQwoAAnTgYcFIZEASsKiEmTWObMmWPF7rFPFKBAgAgwHUGADDS7SQF/ChQVFWHhwoXYuHEjunbt6s9Q2DYFKECBDglw4tQhPu5MAQooCYjUA+IsU1ZWFrp3765UnNspQAEKGFqAl+oMPTwMjgLmFxCpBwYMGIApU6aYvzPsAQUoEPACPOMU8IcAASign8DWrVvxySefYM+ePfo1wpopQAEK+FCAeZx8iO1oinmcHBLafmceJ209nWvzJs/MZ599hrlz58o5X6Kjo52r0/W1N7HqGpBC5WaKl7EqDKaXm83kKroo4mUeJ6smWzBov5jHyX1glPKciD2UyjCPk7urGjc98jidOXNGGjJkiLR+/foWQSmNodJ2Nf1Rk2NGi3a0qEP0RyleLdrRog5fxapmjNX0R8lVq3bUxKJURotYfdkfNfGKeKy68B4nL/9D4G4UoEDrAunp6fJ9TdOmTWu9ELdQgAIUMKEA73Ey4aAxZAoYWcBxX1NOTg5TDxh5oBgbBSjglQAnTl6xcScKUMCTwJEjR5CSkoLCwkKEh4d7KsJ1FKAABUwtwEt1ph4+Bk8B4wicOXMGjz76KNavX89HqhhnWBgJBSigsQAnThqDsjoKBKKAeA7dW2+9xfuaAnHw2WcKBJgAL9UF2ICzuxTQQyAzMxOVlZXYvn0772vSA5h1UoAChhHgGSfDDAUDoYA5BfLy8jB79mzMnDkToaGh5uwEo6YABSigUoAJMFVCaVmMCTC11Gyuiwkwmy20ftVagj5xX9P06dMh0g8MGzZM62a9qq+1WL2qzAc7mSlexqrPAWEmVyEg4mUCTKtmqTJov5gA031glBLEiT2UyjABprurGjdvE2BeunRJTnK5dOlSuWGl8VETixZ1qEnOp0U7WtQhTJTi1aIdLerwVaxaHSdKrlq1o4WtFrH6sj9q4hXxWHXhpTp9/oFgrRSwtIC4GfzJJ5+UbwafM2eOpfvKzlGAAhRwFgiAiZMdFwoWICwoCOISmfyVuBnldicGew1Ks9IxUmwPS8FLxTVw3iyXVFPGqUq+pICVBcTN4OLhvc899xxvBrfyQLNvFKCAm4D1J072k/jgjXdR09R1GxIm3omIpp6fQ+namZhXNgbb6iXUlz6ML9NnYm3puaY9ADVlnIrzJQUsLOC4GfwPf/gDk1xaeJzZNQpQwLNA0/TB82azr7Wj9nAOft/rdzgvSZDkr2rkTo2Go+P28hwsWHsbnpk/GrZgINg2GvOfuQ1rF+Q0nZVSU8bsUoyfAmoERGbwxMRE5ObmYuDAgWp2YRkKUIAClhJwzB8s1anmzpxF8dtvIG/VSizdnIOC8gvNm+RXV1BRuAd5MREID3FQBKP74DGYfHQPCiuuAFBTxqVavqWABQWqqqqaMoMnJCRYsIfsEgUoQAFlAcdsQbmkCUvYy/8vVq4qBZCHVdPGY3TUBKTnHEetoy/2ShRuL4RtYD/0cZMoxPbCStjVlHHUx+8UsKiA3W7HrFmzmBncouPLblGAAuoF3KYL6nc1fsngyKnIlSTUV5dgZ2Ya4sUEavw8bHLcv1RbjbKjQExUGEJa646aMq3ty/UUsIjA559/Lvdk3bp1vBncImPKblCAAt4JBFQCTHvNXiyalIItca/j+MpR6H6hAOnRD+PIkgLsdrrvCc7rH6xGhlIZ530bx2Ho0KGtjkhxcTHi4uJa3c4NFDCSgEgs+tVXX+HWW29F586djRQaY6EABfwkwASYVs1S5daveul8foZks2VI+efrJan+mJSZYJNsafnSeeey5/OlNJtNSsg8JtWrKeO8r4rXTIDpjqRFEjkmwHR3FWuUbNtKgJmdnS2J4/X222/3XLnTWqV21MSiRR1qkvNp0Y4WdQgTpXi1aEeLOnwVq1bHiZKrVu1oYatFrL7sj5p4RTxWXSx9qc59Ih6MkPAIxDhuBg/uhxETR7gVs39RiSM1IzBxRD8EqynjVgNXUMD8AkVFRRg/fjwKCwvRrVs383eIPaAABSiggUCATZzsqK36N2LTf45IueddEDHiXsS89gFKLjhSXooyFTiacC9GRHQBoKaMBiPBKihgIIHy8nKMGDECWVlZGD58uIEiYygUoAAF/Ctg4YlTHWpK38euUkcW8DrUFP8BS/fHYnZ8ryb14MhkLJt7DItX5KPGDthr8rFi8THMXZbcOLkC1JRpqpAvKGByAZF24OGHH8b69esxZcoUk/eG4VOAAhTQVsDCEycA5z/CbweHoVNQEMJS1qGodhSeefEeOdFlM2MPxM59GSt7v47YTkHoNOkDRK15GXNjezQXgZoyTsX5kgImFTh79iySk5PltAMi/QAXClCAAhRoKXBNy7dWetcZtlHPYZ/0nHKngm2Im5OF6jlZrZdVU6b1vbmFAoYXEA/uTU9PlydNIu0AFwpQgAIUcBew8MTJvbNcQwEKeBa4cuUKnnzySXz55Zd48803mavJMxPXUoACFEBA5XEyyngHBQVhx44dRgmnzTiWL1+OjIyMNssYZaPIN3Tw4EEkJSUZJaQ24zCS7caNG1FZWYn58+ejZ8+ebnEbKVa34FxWmClWEbqZ4mWsLgebRm/N5Oo4ZpnHyarJFgzaL+Zxch8YLXKhMI+Tu6tYo2T77LPPSjExMdLJkyc9V6Ai15CadtSUUYpVTR1qcsxo0Y4WdYj+KMWrRTta1OGrWNWMsZr+KLlq1Y6aWJTKaBGrL/ujJl4Rj1UXXqrT6D8GVkMBMwps2LABL774Ij788EOEh4ebsQuMmQIUoIBPBaz9qTqfUrIxCphLQEyaZs+ejbfeegt9+vQxV/CMlgIUoICfBHjGyU/wbJYC/hTYunWrPGkSWcFvvPFGf4bCtilAAQqYSoBnnEw1XAyWAh0XEI9SSUlJkR+lwqzgHfdkDRSgQGAJcOIUWOPN3ga4gJg0iUepiDNNnDQF+MHA7lOAAl4JcOLkFRt3ooD5BDhpMt+YMWIKUMB4Apw4GW9MGBEFNBfgpElzUlZIAQoEqAATYPph4JkAUx90JsD07JxCzqcAACAASURBVHr8+HE5ialIshcdHe25kMJaMyXoM1Osgt1M8TJWhR8ULzebydVxzDIBplWzVBm0X0yA6T4wSgnixB5KZZgA0921sLBQEseb+N7aUl5eLomvthY1Ce+UxkfUr1RGabuaOswUq+iPUrxamGhRh69iVTPGavqj5KpVO2piUSqjRay+7I+aeEU8Vl14qc7L/xC4GwWMLuC4PCf+m+WN4EYfLcZHAQqYRYB5nMwyUoyTAu0QcEyaxKfnxIN7uVCAAhSggDYCPOOkjSNroYBhBERGcKYcMMxwMBAKUMBiApw4WWxA2Z3AFnA8RoV5mgL7OGDvKUAB/QQ4cdLPljVTwKcCnDT5lJuNUYACASrAiVOADjy7bS0BMWkSz5/jmSZrjSt7QwEKGE+AeZz8MCbM46QPeiDmcaqrq8Mrr7yCyspKzJ8/Hz179tQF10x5ZswUqxgsM8XLWHX58TLVMeA4ZpnHyarJFgzaL+Zxch8YpTwnYg+lMoGWx+nSpUvSmDFjpCFDhkgnT550R21co+TGPE6e6ZTclLarOWZFGaWcOFq0o0UdvopVjZua/ii5atWOmliUymgRqy/7oyZeEY9VF16q0+cfCNZKAV0Fqqqq8NBDD8lt5OTkIDw8XNf2WDkFKEABCjQIcOLEI4ECJhMQk6bk5GT07t0bM2bM4KTJZOPHcClAAXMLcOJk7vFj9AEmIBJbiklTfHw81q1bh86dOweYALtLAQpQwL8CnDj515+tU0C1QF5enpzYcsqUKVi1ahW6du2qel8WpAAFKEABbQQ4cdLGkbVQQDeBy5cvY9myZUhMTERubi5mzZqlW1usmAIUoAAF2hbgs+ra9uFWCvhV4IsvvkBqaiqqq6tRVlaGyMhIv8bDxilAAQoEugDPOAX6EcD+G1ZAXJr7yU9+Ik+WDhw4wEmTYUeKgVGAAoEkwASYfhhtJsDUB90qCTAvXrwIkWJg586dSE9Px7Bhw/QBa0etTHzYDqx2FqVtO8FUFqerSigviglbJsC0apYqg/aLCTDdB0YpQZzYQ6mMFRJg5ubmygktp0+fLn344YeSSE7Z1qJkosaNCTA9CyvZKm1XYy/KKCUT1KIdLerwVaxq3NT0R8lVq3bUxKJURotYfdkfNfGKeKy68FKdF7Nt7kIBrQXOnj2LtLQ0+QZwcfO3SDXQp08frZthfRSgAAUo0EEB3hzeQUDuToGOCoh7mRYtWoSwsDDeAN5RTO5PAQpQQGcBnnHSGZjVU6A1gW+//bbFWaY333yTN4C3hsX1FKAABQwiwDNOBhkIhhFYAuLm748//hiDBg3iWabAGnr2lgIUMLkAJ04mH0CGby6B8vJy+SyTyMt066234pVXXjFXBxgtBShAgQAX4KW6AD8A2H3fCIibv0X276ioKPly3J49e3DDDTf4pnG2QgEKUIACmgnwjJNmlKyIAp4FxGW5FStWyDd/Hz58GAMHDvRckGspQAEKUMDwAkyAqdMQDR06tNWai4uLERcX1+p2brCGQG1tLWpqalBXVydPmniGyRrjyl5QgAJgAkyrJqkyar+YANN9ZJQSxIk9lMoYJQFmWVmZNG7cOEmM8/r166UzZ864d1hF4kM1iSmVTNS4qWlHTcI7LWLRog4zxSrGRyleLUy0qMNXsao5ZtX0R8lVq3bUxKJURotYfdkfNfGKeKy68B4n/utAAY0EnO9jElWKh/KKZJahoaEatcBqKEABClDA3wKcOPl7BNi+6QXEhGnDhg3o2bMnxGVYMWFKSUlhTibTjyw7QAEKUMBdgDeHu5twDQVUCVy+fBm7d+9uuvG7sLAQw4cPl/f9xz/+oaoOFqIABShAAXMJcOJkrvFitAYQuHLlCg4cOICnn35ajmb+/PlITk42QGQMgQIUoAAF9BbgxElvYdZvGQHHGaYlS5ZATJ7E97Fjx6Jr166W6SM7QgEKUIACbQtw4tS2D7dSAI4Jk8jFJBZxpummm27CyJEjqUMBClCAAgEmwDxOfhjwoKAg7Nixww8tt7/J5cuXIyMjo/07+mGP06dP4+DBg0hKStKk9YsXL6KkpATvv/++XN/48ePlZ8t17txZk/rNZMtYNRlyj5XQ1iNLh1fStcOErVYgbA8dOtTqdstvsGqeBSP3i3mc3EdHKc+J2EOpjFZ5nLZu3SrnXxLjlJSUJGVnZ0uXLl1qClrkZSoqKmp67+mFUqxiH6VcKGryK6lpR6mMmnaUYhX9UWpHTRkt6jBTrGqOAy1MtKjDV7FqdZxocRxo5aZUjxaxauWmFKua40CUsfLCS3WWnxqzg2oFxAN48/LyMHv2bPmslfOn5NTWwXIUoAAFKGBtAeZxsvb4sncqBI4cOYK0tDT5Abz/+te/IE5D79y5sym1gIoqWIQCFKAABQJEgBOnABlodrOlgLjhu6ioCOPGjcOPfvQj9OjRQ05cuWrVKkRHR7cszHcUoAAFKECBRgFequOhEFAC4obvnJwcOWml6PiUKVOwefNmPhYloI4CdpYCFKCA9wKcOHlvxz1NJOB6/5JIWskcTCYaQIZKAQpQwCACvFRnkIFgGPoIiMtxM2bMcLt/SWT6ZuJKfcxZKwUoQAErC3DiZOXRDdC+iYfubt26FXFxcRgxYgQGDBiAkydPgvcvBegBwW5TgAIU0FCACTA1xFRbFRNgqpVqXzmRrFI8dPfjjz+WJ00is/egQYOgVcLK9kWjXJoJ+pSNvClhJlfRPzPFy1i9OSKV9zGTq+OYZQJMK2eqMmDfmADTfVDUJF3zVEYkphQJKkWiSuE6fPhw6fDhw+4NNK7xVIdrYaUyTIDpKtbwXslNlFIqo7RdTR1WSyaohYkWdQh7JVut2lGqR2m7mljVHEtq2tGijJKrmljVlNEiVrW2opxVF16qU/5ngCUMKCBu9t6wYQO6desmf0JO3LMkzjglJCRg4MCBBoyYIVGAAhSggBUEOHGywigGSB/q6urkzN4i91JUVBREskqR3bu4uFhOKyByMXGhAAUoQAEK6CnAdAR66rJuTQScUwkMGTIEs2bNYu4lTWRZCQUoQAEKtFeAZ5zaK8byPhEQmb3Fc+Oczy6JGygdZ5dCQ0N9EgcboQAFKEABCjgLcOLkrMHXfhcQz41z3Lu0aNEiiHuXzpw5w1QCfh8ZBkABClCAAkKAEyceB34XEHmXDh482PTcONd7l3h2ye9DxAAoQAEKUKBRgPc48VDwm4A4u/T+++9j4cKFiIiIwDPPPMN7l/w2GmyYAhSgAAXUCDABpholjcsEcgJM8ZDdv//979i3b598v9KvfvUr3H777YiOju6w8unTp+UzV0lJSR2uyxcVmCnpHWPV74igrT62dNXHVdQqbJkA06pZqgzar0BMgLlp0yZp6dKlcpJKkaxSJK0UiSQdixaJ2SoqKqQXXnjBUaXH71q0wwSYHmkVk1uKvZT8lbarqcNqyQS1MNGiDmGvZKtVO0r1KG1XE6uaY0lNO1qUUXJVE6uaMlrEqtZWlLPqwkt1+k3KA75mce/Se++9h9/+9rc4fPgwli5dKn9ngsqAPzQIQAEKUMC0Apw4mXbojBt4UVERdu3ahdWrV0NcNnv66adx44034t577zVu0IyMAhSgAAUooEKAn6pTgcQiygLi7NLWrVvlh+uOGDECIou3OMu0c+dO/OxnP0P37t2VK2EJClCAAhSggMEFeMbJ4ANk9PBEVu933nkHDzzwgHx2af78+YiPjwdTCBh95BgfBShAAQp4I8AzTt6oBfg+rlm9v/nmG/mZceLskkhYyUlTgB8g7D4FKEABCwtw4mThwdW6a+LsknNW7zFjxuDkyZNISUnB8OHDtW6O9VGAAhSgAAUMJ8A8Tn4YEjPlcVq8eDHuueeeprxLYrI0evRo9O/fH507d/aDXutNMo9T6zYd3cKcOB0VbH1/2rZu05EtdO2IXtv7Mo+TVRMtGLhfRs/jdOnSJSk3N1eaPn16U96lrKws6eTJkx5VlXKDaJX3SKkd5nHyODyKuZPKy8sl8dXWYqY8M2aKVZgrxat03Is6lMoobVdTh69iVROLmv4ouWrVjppYlMpoEasv+6MmXhGPVRfeHN72xDpgtopPxZWUlMhf4hEoQ4YMwZQpU+Ss3uLeJS4UoAAFKEABCvAhvwF9DFRXV+PAgQOYMWMGevbsiUWLFslpA0QageLiYsyaNQvdunULaCN2ngIUoAAFKOAswJvDnTU8vq5DTelrSB8ZhqCgGKS8VIQau8eChl8pziqJ5JTiBu9x48YhJiYGu3fvxl133SXnXHJMlpjZ2/BDyQApQAEKBJxAXl4ecnJyID7Z7c+FE6c29e2oLd2ISfNOIHFbJaT6PUj5cjkmrS1GbZv7GWOjeKCumCiJxJSOs0oiOeWFCxcwc+ZMHD16FCtWrJAvyXGyZIwxYxQUoAAFKOBZ4LrrrpP/Zt19993y3zbPpfRfy3uc2jK2l+PtBe8g7pldGGUTnyDri1Hz5yI3eg3e/vlWTI3s0tbePt0mZuAiNcCnn36K48ePyxm7P/roIzmG1NRUjB07FuJ7ZGRkU1ziDJSYRHGhAAUoQAEKGF1ApL0Rt5dkZmZCnAQQf9OmT5/e4u+aL/rAM05tKNsr/oLteX0RFR7SXKr7HUicfArbCyvhjyt2VVVVEPmUjhw5Ip9JSktLkx9zIu5FioqKki+9icebLFmyBK+++iokScKqVavkxJTOk6bmDvEVBShAAQpQwBwCXbt2le+/FScKxCL+7onbT8SJAF8tPOPUqvQVVBTuQZ4tAul9XPMVXUXe9r+g4pFoRHo59RSTH0/LpUuXcOLECfnmbLvdjoMHD8rF9u/fD8cZJLEiLi4O4nTlsGHD5Eed9O7d223WbZRPw4kD/eabb/bUXVOuE/255ZZbTBm7nkGL++aUFqUySttF/WrKKMXhq+28BO4u/cMf/tB9pYnXiE8gc/G9QHh4uHxSYNKkSXj++eflEwnikV/i6RV6L5w4tSpci6qyE0DMvQgPaf/sSCS5bGsRs+SOLOJGbvHli0WpL76IoT1tPPfcc+0p7teyZrJlrPodKrTVx5au+riKWo1oO378eCxduhQLFizQr+NgOgLdcMUlsta+RKOtbTPaenFmy2gxtRZPRUUFXnjhBdPEayZbxtr6z3Nrx6Pa9bTVx5au+riK49pItrm5uXLeQXHmr7CwUPdJk/j73f5TKbpNNYxWcQjCo/oDRytQVeuPu5mM5sF4KEABClCAAsYQELe7iE+LJyYmyvc8iZvGffXMVE6cWj0GuiBixL1IcN1u/wqVR84hYeKdiKCeqw7fU4ACFKAABXQTEDeBL1u2TL4p/IYbbsCZM2fklDri3lNfLfzT34Z0cMSdmBhzALklTnfr11aj7OggTBzRj6fr2rDjJgpQgAIUoICWAiIBpnjKhbi/t6ysTL45PDQ0VMsmVNXFiVNbTMGR+MWyB1G8eCMKauoA+ykUrFiL4rnz8AsD5XBqqwvcRgEKUIACFLCCgEiAKe5pEp8Y92d6HU6c2jyaghES+wS2reyFrNhrEdRpKnKjnsW2uXFwyuzUZg3cSAEKUIACFKBAxwXEPUwJCW430HS84nbWwHQEimCdYYt7AlnVTyBLsSwL+FNAnLIdNGiQP0Ng2xSgAAUoYHGBIEl8tpALBShAAQpQgAIUoICiAC/VKRKxAAUoQAEKUIACFGgQ4MSJRwIFKEABClCAAiYUOImclAg5i3lQ0M+wpvQcYK9B8UspCAsKQsSaUl36xEt1urCyUgpQgAIUoAAFfCFgP5WDGUPGY/fkt5DV5zhOjp2DqdHddWuaEyfdaFkxBShAAQpQgAL6C3yFgvR7MXrVVUzNfg+vJN+sa55FXqrTf0TZAgUoQAEKUIACugmEYnBiAmy4DcNv/y9dJ02iC5w46TaQ7hXba4qRlZ4oX48NS9mIYpFUk0s7BeyoLc/FmpSYxuvaiUjPKkaN2+ME61BT+hrSR4YhKCgGKS8VeSjTzqYDqngdTuXMQljiZpS72tprUJqVjpFBQQgKS8FLxTVwLRJQVO3qrDgu38c7axruwQhLL8CFpv15zDZRqH5xAeV7X0JKWFDD74OwFKzZW45al/35u9cFxPVtbTkKcrZhTUoi0gu+ct3a8F7Nz72aMp5r7+Dab3HxnPhJKsT2wkrdfx9x4tTB4VK9e20x1k56EWWJm1EvXUVpyldIn7QRpXyAsGpCUdB+ag9e+TPw842fQJKuovrQz/FFxjhMWlvs9MvSjtrSjZg07wQSt1VCqt+DlC+Xu5RpV7MBV9h+6j08O2sjatx6fg6la2diXtkYbKuXUF/6ML5Mn4m14qZMLm0LyDetzkDs/dtR2e/X2H+xHtUrR6HhTgwes23jedoqJvcLEJ/yKe4uOA+RWUccj2eX/RqLnf/483evJ7zmdfbj2PzLRcjKXo7UrWea17d4pebnXk2ZFpVq9kb8vlr852vxUDxwtKza6W+BZk20rEjkceKit8BlqSxzgmRLy5fONzX1pZSfdqeUkHlMqm9axxdtC1yWKvb9VapqAdZgC1uGlH++cUP9MSkz4U4pLf/L5urO50tptglSZtnl5nV85Vng4iFp9ZSnpLQpt0tIyJTKnLzryzKlBGdrqV46n58h2VzKea44kNd+LZWs/qlkm7JBOlR91R2Cx6y7idIa2czm8nvV9Xet63tRKX/3eqKVf7YR2/L3ZmNBNT/3asp4arfD6+orpezH0qTsqvPy31n5b0HVX6W1GTtd/lZ0uKWmCnjGqeU8Up939koUbv8YMVFhTo9qEddk78bR7X9BBa9zqHTvglvih6Fvi6O2M/r0i4DNqQZ7xV+wPa8vosKdHozT/Q4kTj7lk9O4TqGY8OU5lG7aBjw5E4l9rnWJ/woqCvcgLyYC4SGOQQhG98FjMPnoHhRWXHEpz7cNAuJs0h8xb20/bFg2A3G2zm4wPGbdSJRXBPdCv4FhqCn+BP+v6cx9LarKLmFy4h0NZ/L4u1fZUbGEmp97NWUUG2pfgW9LsSYiCEGjfw/MXYjkviEIG/BjxNdsweJ11fjpgvtd/la0r/q2Sjt++7VVhts6KNDwS7EHBvbr5X5TWR7/4HSQV96929jBiJL/mDf+ANsi0K+P6x+oq8jjRLUNbvEHfivWYRIej/XwxHH5j1AhbAP7oY/bbw7f3FvQRvDG3WQvx9sLNgKTB8D+5gw5v4y4N6z5Xhwes94NXijifvErxO+fi/ufeA3Ha6+gpmALcvtk4On4XnKV/N3rnWyLvdT83Ksp06JSDd5cE4t5FRKkfcuQHCkueItny87BPqka+1YmI7LpnzsN2nKpwu3Xn8t2vu2wgB21VRU4iv4tz4B0uF5W0CBwFiW5p/D4zFGN/12I/zhPAC3OitBKlUBtCTatA558fLDTmVGnPWurUXYULmdOnbbzpUeBhj/etyDuBwMwfG4WqqXzOLbkGqxNmItN8r1hPGY9wimubHwI+6ENuGfvI7jt+v54pPJnWD5nOGzyXzb+7lUkVFNAzc+9mjJq2jJJGU6cTDJQDNOTgDhDsg1ZvZ/A47E9PBXgOtUC51D6SgH6L3scsTr+p6Y6HMsUbPzjbYtF4gODG/+gd0f0I6lYkvAxUhfkuH9q0TJ990VHrsH1PcIRM3c50uKBvGlPYVHBKd0/VeWLnrEN4wpw4qT72AQjJDwCMTiBsirXD8nq3ri1G6gtwStv34CMFmdIQhAe1R84WoGqpvserM3Q8d6JCehbyL75IYzr63p506n2kDBExfjoUytOzZr7ZR2+qKxw/3RicD+MmDii8TjtxmPWq0G2o/b4a3hqbT0emjsfK/M/Qn4GsHz0Y42f8uTvXq9YXXdS83OvpoxrvSZ+z4mTDwYvOOJOTExwvdG28Rdqwr0YEdHFB1FYrAn759j1ymcY+8yvEN3iDEkXRIy4Fwmu3bV/hcoj55Aw8U5E8Kh30TmL4rdfxfLx/dBJ5GaSv3pj9KpS8S88ojqFIXHzcdgdf+xd9rZ/UYkjNSMwcUQ/93v4XMoG3tvGDy/UVKDyCw952+RLyt14zHpzYIh7x55ajKq4HzScyQvui1HLtqNkNZrO5PF3rzewLvuo+blXU8alWjO/5Z8QX4yefFD1xWu5f3NKdifuazjFP+Te+NtPoeB3u3H9Lx9onjTVfoqszUWyr/zLMuYAckvONtcuX4MfxD/uzSJOr3ph1MoSOQ+OyIXT8PUl8tNigYRMlNVXI3dqNILRMCmNee0DlFxwfBS08VIU/wFw8nR+2fipQ9sxFH162ukSUsuffx6zzmYqX8s/05dcCnfHrYPuaP6ULX/3uvh481bNz72aMt60bdB9mhIT8IW+AiI3TvxPpYz8KqleuipV5z8vxcevlUouOiXJ0TcCa9R+8ZiUnZYgAXD5sjnlxKqXLpasleLjn5fyRc6c+iopP+OnUvzqQ9JFayj4oBci102sWx4nSRL5iMZJ8Rl5UnW9JNVX50kZ8eOk1SVf+yAmszZxVarKfkKy2aZKmcdEJrerUvWhDdKUBOeffx6z7R/dhtxYaHKVJOniUSlzSrw0NbuyOT8ef/eqom0rj5O6n/vA+d0g/rvk4iOB+upCaa1IKgibFJ+2VSrxlAjPR7GYshmR6Gyq8HOdNIn3rsktG/842cS2BCltyyH5D70p++2XoFubOElitiQdWjtFsolxiE+TtpRUN/+R8kusZmj0vFSWt1aaIh+Prf3885ht90jWV0slW9KkeMfvBNsUaXVemds/SPzd25Zs48+6w1B895TQVs3PvZoybYVikm1BIk6DngxjWBSgAAUoQAEKUMBQArzHyVDDwWAoQAEKUIACFDCyACdORh4dxkYBClCAAhSggKEEOHEy1HAwGApQgAIUoAAFjCzAiZORR4exUYACFKAABShgKAFOnAw1HAyGAhSgAAUoQAEjC3DiZOTRYWwUoAAFKEABChhKgBMnQw0Hg6EABShAAQpQwMgCnDgZeXQYGwUoQAEKUIAChhLgxMlQw8FgKEABClCAAhQwsgAnTkYeHcZGAQpQgAIUoIChBDhxMtRwMBgKUIACFKAABYwswImTkUeHsVGAAhSgAAUoYCgBTpwMNRwMhgIUoAAFKEABIwtw4mTk0WFsFKAABShAAQoYSoATJ0MNB4OhAAWEgL18MxKDBiO94CuNQeyoLc/FmgXbUG5vqFq/tjQOXaPqGvr7C2wuv9JQY2059q5ZiizHe43aYTUUsKoAJ05WHVn2iwImFgiOnIpcqQQrR/XSuBdnUZy5EKmljZMGAPq1pXHoulRnx4XiLUhJ/QT1utTPSilgPQFOnKw3puwRBShAAQpQgAI6CXDipBMsq6WAoQXsNSjNSsfIoCAEia+R6dhcUI5aOWg7aktfwsigGEzL+RyNV7SA2mKsGRmGsGk5OCWvrENNaQ7WpMQ01OGhngsFCxAW9ADW5DiXS0R6VjFqLohLRCkIk2OIQcpLRajxePnsKxSkD0ZQ4kYUFL+G9JFhDe2FpWDNXkfMDdr2mlLkNNUp+paI9M0FKK8VFYt67sXoVaVA3jREdWq4FOjxUl1tOQo2t+YD4EIB0sPCkPjKXhQ7OYalvIS95RdaH/rG/Uamr2tyC0svgLxHm2MiqhSXGQuwOT2xFe9Gp7AFKLjQNGqNsQahqZ2m6Oy4ULAI0aOXowZ/wrSoro1llNppqoAvKBCQApw4BeSws9MBLWD/HDkzEnB/wfewsvoqJKkeF//nBzjw8Hg8JU+UghES+2usWX0zNs9ajZ2n6gCcQ+mmF5FalowNL/4MfYPF5GojJt2/C52eyEO9JEGSrqL6mW54bfRcbCo950S8E6nrS9B/YVFDmfw7UfzIUIRFL8WnP1mBKtH+sXnA6sexaKfTRM2pBvll3lIszr4O096taqjn9f74c4JTW7XFWDvpMezq9ChK60U8Euqr56HTa4/isU0lqEUvjFq5B/lpsUBCJsrqW7kUWPspNj8xHg8fcPhcRfXK7+HAw/G4f01x4+RSRFSDvEfXIPv6X+Nd0f/6Krzedw8SHstEqTxRc+2A430N9r/2CUIziiDVn8b+Rweju+KYAKgtwabH0nAg6v/gYgvvRXjbq/uTgtF91BIcz8+ADROQWXYZ1StHobvm7Tj6ze8UsIYAJ07WGEf2ggIqBey4sP/3mLX5NixZOA1xts7iLh+ERE/G+tfvx+5Zv8d++WxFD8Q+/ixWR+Vg1rP/F8eL/4h5qZ9j6oZUjOsr9jmL4rffQNnkFEyLs6HhF0ln2OInYnLCcez95IvmM1WIRdozc5Ec2R1AZ9gG34U4mw0JSzLwlLxvMEIih+LumDPYfeifThMTly7ZHsEzC8chMkS05qjn48a2xL06O7G2LAEp034MW+NvtmDbXXhk8iDs3/spqp1OwrjU7PRW1LMNi/bejQ3LZjT6dIYt7jdY//ojKEtd02KSYktLx8LkaISIGoJtGDwmFrb9f8Un1WKy2fpim/wrPBjdHQi+EZG3hKgaE3v1p9i7vz/uHhHR0J4wGPUc9klvY2pkl9Yba+cWX7XTzrBYnAKGEeDEyTBDwUAo4AuBsyjJzUONLQL9+ogJkGMJRkh4BGJq8pBbcrZhZchgPL4mFVGbJ+C2oauB1Zn4XfLNjZMkcfamBNUrB+OLgl3IyclBTs4rSB89CtPyLjkq1fd7SBiiYoCjZdWohTh7sgzV1UsQ98WHjfG8g83pSYia9qd2xNHoEzMIt8uTSseujT44gbKqhguaji3N39WUaS7d/ErdmASH3Y574guxKPM9FBe8h4K2Lgk2V97uV75qp92BcQcKGESAEyeDDATDoIBPBWqWY/R3OzXfKxMUhE5R05DXIohghPwoGbOn3g5gEH46MrLxTIcoZEft8SykhH0XUaNfxqFz4nTOjUj8nxxkJjgmM47K+iMqXD4n41ihz3dx1t9ySgAABHxJREFUiS1lAK6PmoT1h87IZ9J6JK5CSeYE4GgFqtq8fNYYkv0rVB6pbiO+ahyp/MrpbFobRdu7SWlMQuIw7939eH3o18he/ChGR33X5R6u9jbYSnlftdNK81xNAaMLcOJk9BFifBTQQ0C+x6fhPiBxL1Dzl/N9P3U4tXM1Zm2+FvHxx5E674/N9+7Yy/H2UxnYOzYbVfW5WDn1QSQnJ2FU2CWUHa3RI2KFOq+g/O0XMW3v3ciuqsS+lTOQnJyM5FF9cb7shMK+TpuDe6HfwDCnFa4vwzCwX6/Gs26u2zr4Xs2YhERiVPIMrNxXDam+GiXZ9+CLRaMRv3h/ww3mHQyhaXdftdPUIF9QwDwCnDiZZ6wYKQU0EAjF4MQE2I5+jE9rnO/DcXySrjkxov3Ue3h2Vg6iVr+MXa+vwtSy1Zgn32QtblSuRtlRIGb4D5ruJxLB2S+eg9YpK9V1uhZVYoLkeonN/g3OfXVVXRVyqTZ8qipwFHqcPWujTfnTjc1j0qIjwTbEJj+ClMmxqDlSiS/sIQiP6t+iiCZv3NrRpFZWQgHTCnDiZNqhY+AU8EYgGN3jH8OGsQcwa8ErKJYnT+Lj5zuxeN5GYPU8/ELcaGz/HDuffQ6bo1Kx5vHB6N73Z3hxQzLKUl9s+MRc9zuQODkMea9tx/7GCZi9pgi/W/AcNvvjhBMaJx9527Fl/6mGS2n2GhT/7lnM2vypE5Tz5OIKamu/ddomXgaje9wkLLnHxef4a5j98BZEOXxc9urYW3Vj0pA2IRHpOceb00aUf4jcYmDqY6MREdwFESPuRULNu8h65x8NZWqPI2fpSqxqdUwc92WJHthxqfYSvpWztrfVTsd6y70pYHYBTpzMPoKMnwLtFQi+Gcm/y8brd/8L6WHXIiioE66P34Xes7dj29w4hMBxie5mrF7za8Q2foqt77hUbJj6eeMlu1DEP/0ytsT9BaPlOoIQPv+vuCnlZWSLj/v7fBGTj9l4d8tA/HV0ODqJ3FDh8/HhTSnYmZ0GW1M8XRAxdgYy6hYhqlN/jH+7wv1+pZDbMXWji89v/oG7X9+Pd+cJHx0WxTERGc4fxpaSx9B71wRcL+e+cozb77FkXMNN+8GRD2J93lRgUUxDmfv/iIvj5+EPCc0CrtEHRyQiPeM8pkVdh+vGv4UTEcrtuNbB9xQIJIEgSdzcwIUCFKAABShAAQpQQFGAZ5wUiViAAhSgAAUoQAEKNAhw4sQjgQIUoAAFKEABCqgU4MRJJRSLUYACFKAABShAAU6ceAxQgAIUoAAFKEABlQKcOKmEYjEKUIACFKAABSjAiROPAQpQgAIUoAAFKKBSgBMnlVAsRgEKUIACFKAABThx4jFAAQpQgAIUoAAFVApw4qQSisUoQAEKUIACFKAAJ048BihAAQpQgAIUoIBKAU6cVEKxGAUoQAEKUIACFODEiccABShAAQpQgAIUUCnAiZNKKBajAAUoQAEKUIACnDjxGKAABShAAQpQgAIqBThxUgnFYhSgAAUoQAEKUOD/A8aeLGpYJlJAAAAAAElFTkSuQmCC"></p>
</div>

<div class="specification">
<p>350 of the group obtained the highest possible grade in the examination.</p>
</div>

<div class="specification">
<p>The grouped frequency table summarizes the examination results of this group of students.</p>
<p><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the median of the examination results.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the interquartile range.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the final examination result required to obtain the highest possible grade.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the modal class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the mid-interval value of the modal class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate an estimate of the mean examination result.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate an estimate of the standard deviation, giving your answer correct to <strong>three decimal places</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The teacher sets a grade boundary that is one standard deviation below the mean.</p>
<p>Use the cumulative frequency graph to estimate the number of students whose final examination result was below this grade boundary.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A company performs an experiment on the efficiency of a liquid that is used to detect a nut allergy.</p>
<p>A group of 60 people took part in the experiment. In this group 26 are allergic to nuts. One person from the group is chosen at random.</p>
</div>

<div class="specification">
<p>A second person is chosen from the group.</p>
</div>

<div class="specification">
<p>When the liquid is added to a person’s blood sample, it is expected to turn blue if the person is allergic to nuts and to turn red if the person is not allergic to nuts.</p>
<p>The company claims that the probability that the test result is correct is 98% for people who are allergic to nuts and 95% for people who are not allergic to nuts.</p>
<p>It is known that 6 in every 1000 adults are allergic to nuts.</p>
<p>This information can be represented in a tree diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.31.34.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c.d.e.f.g"></p>
</div>

<div class="specification">
<p>An adult, who was not part of the original group of 60, is chosen at random and tested using this liquid.</p>
</div>

<div class="specification">
<p>The liquid is used in an office to identify employees who might be allergic to nuts. The liquid turned blue for <strong>38 </strong><strong>employees</strong>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that both people chosen are <strong>not </strong>allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy </strong>and complete the tree diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this adult is allergic to nuts and the liquid turns blue.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the liquid turns blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the number of employees, from this 38, who are allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>In a company it is found that 25 % of the employees encountered traffic on their way to work. From those who encountered traffic the probability of being late for work is 80 %.</p>
<p>From those who did not encounter traffic, the probability of being late for work is 15 %.</p>
<p>The tree diagram illustrates the information.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The company investigates the different means of transport used by their employees in the past year to travel to work. It was found that the three most common means of transport used to travel to work were public transportation (<em>P </em>), car (<em>C </em>) and bicycle (<em>B </em>).</p>
<p>The company finds that 20 employees travelled by car, 28 travelled by bicycle and 19 travelled by public transportation in the last year.</p>
<p>Some of the information is shown in the Venn diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>There are 54 employees in the company.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>a</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>b</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee&nbsp;encountered traffic and was late for work.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee&nbsp;was late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee&nbsp;encountered traffic given that they were late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>y</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {\left( {C \cup B} \right) \cap P'} \right)"> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <mi>C</mi> <mo>∪</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> <mo>∩</mo> <msup> <mi>P</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Adam is a beekeeper who collected data about monthly honey production in his bee hives. The data for six of his hives is shown in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.46.13.png" alt="N17/5/MATME/SP2/ENG/TZ0/08"></p>
<p>The relationship between the variables is modelled by the regression line with equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P = aN + b">
  <mi>P</mi>
  <mo>=</mo>
  <mi>a</mi>
  <mi>N</mi>
  <mo>+</mo>
  <mi>b</mi>
</math></span>.</p>
</div>

<div class="specification">
<p>Adam has 200 hives in total. He collects data on the monthly honey production of all the hives. This data is shown in the following cumulative frequency graph.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.49.33.png" alt="N17/5/MATME/SP2/ENG/TZ0/08.c.d.e"></p>
<p>Adam’s hives are labelled as low, regular or high production, as defined in the following table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.51.25.png" alt="N17/5/MATME/SP2/ENG/TZ0/08.c.d.e_02"></p>
</div>

<div class="specification">
<p>Adam knows that 128 of his hives have a regular production.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
  <mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this regression line to estimate the monthly honey production from a hive that has 270 bees.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of low production hives.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span>;</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of hives that have a high production.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Adam decides to increase the number of bees in each low production hive. Research suggests that there is a probability of 0.75 that a low production hive becomes a regular production hive. Calculate the probability that 30 low production hives become regular production hives.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the following frequency table.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_09.52.57.png" alt="M17/5/MATME/SP2/ENG/TZ1/01"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the mode.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of the range.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the mean.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the variance.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights, in grams, of oranges grown in an orchard, are normally distributed with a mean of 297 g. It is known that 79 % of the oranges weigh more than 289 g and 9.5 % of the oranges weigh more than 310 g.</p>
</div>

<div class="specification">
<p>The weights of the oranges have a standard deviation of σ.</p>
</div>

<div class="specification">
<p>The grocer at a local grocery store will buy the oranges whose weights exceed the&nbsp;35th percentile.</p>
</div>

<div class="specification">
<p>The orchard packs oranges in boxes of 36.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that an orange weighs between 289 g and 310 g.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the standardized value for 289 g.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the value of σ.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>To the nearest gram, find the minimum weight of an orange that the grocer will buy.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the grocer buys more than half the oranges in a box selected at random.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The grocer selects two boxes at random.</p>
<p>Find the probability that the grocer buys more than half the oranges in each box.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A factory manufactures lamps. It is known that the probability that a lamp is found to be&nbsp;defective is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>05</mn></math>. A random sample of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> lamps is tested.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that there is at least one defective lamp in the sample.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that there is at least one defective lamp in the sample, find the probability that there are at most two defective lamps.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The weight, <em>W</em>, of basketball players in a tournament is found to be normally distributed with a mean of 65 kg and a standard deviation of 5 kg.</p>
</div>

<div class="specification">
<p>The probability that a basketball player has a weight that is within 1.5 standard deviations of the mean is <em>q</em>.</p>
</div>

<div class="specification">
<p>A basketball coach observed 60 of her players to determine whether their performance and their weight were independent of each other. Her observations were recorded as shown in the table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>She decided to conduct a <em>χ </em><sup>2</sup> test for independence at the 5% significance level.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a basketball player has a weight that is less than 61 kg.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In a training session there are 40 basketball players.</p>
<p>Find the expected number of players with a weight less than 61 kg in this training session.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch a normal curve to represent this probability.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>q</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that P(<em>W</em> &gt; <em>k</em>) = 0.225 , find the value of <em>k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For this test state the null hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For this test find the<em> p</em>-value.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a conclusion for this test. Justify your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The weights, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="W">
  <mi>W</mi>
</math></span>, of newborn babies in Australia are normally distributed with a mean 3.41 kg and standard deviation 0.57 kg. A newborn baby has a low birth weight if it weighs less than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
  <mi>w</mi>
</math></span> kg.</p>
</div>

<div class="question">
<p>Given that 5.3% of newborn babies have a low birth weight, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
  <mi>w</mi>
</math></span>.</p>
</div>
<br><hr><br><div class="specification">
<p>160 students attend a dual language school in which the students are taught only in Spanish or taught only in English.</p>
<p>A survey was conducted in order to analyse the number of students studying Biology or Mathematics. The results are shown in the Venn diagram.</p>
<p>&nbsp;</p>
<p style="padding-left: 240px;">Set <em>S</em> represents those students who are <strong>taught</strong> in Spanish.</p>
<p style="padding-left: 240px;">Set <em>B</em> represents those students who <strong>study</strong> Biology.</p>
<p style="padding-left: 240px;">Set <em>M</em> represents those students who <strong>study</strong> Mathematics.</p>
<p style="padding-left: 210px;">&nbsp;</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>A student from the school is chosen at random.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that&nbsp;are taught in Spanish.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that study Mathematics in English.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of students in the school that study both Biology and Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {S \cap \left( {M \cup B} \right)} \right)">
  <mi>n</mi>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>S</mi>
      <mo>∩</mo>
      <mrow>
        <mo>(</mo>
        <mrow>
          <mi>M</mi>
          <mo>∪</mo>
          <mi>B</mi>
        </mrow>
        <mo>)</mo>
      </mrow>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n\left( {B \cap M \cap S'} \right)">
  <mi>n</mi>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>B</mi>
      <mo>∩</mo>
      <mi>M</mi>
      <mo>∩</mo>
      <msup>
        <mi>S</mi>
        <mo>′</mo>
      </msup>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student studies Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student studies neither Biology nor Mathematics.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this student is taught in Spanish, given that the student studies Biology.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>Lucy sells hot chocolate drinks at her snack bar and has noticed that she sells more&nbsp;hot chocolates on cooler days. On six different days, she records the maximum daily&nbsp;temperature, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>, measured in degrees centigrade, and the number of hot chocolates sold, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math>.&nbsp;The results are shown in the following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The relationship between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> can be modelled by the regression line with&nbsp;equation&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>a</mi><mi>T</mi><mo>+</mo><mi>b</mi></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the regression equation, estimate the number of hot chocolates that Lucy will sell on a day when the maximum temperature is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>°</mo><mtext>C</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> be two independent events such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>&#8745;</mo><mi>B</mi><mo>'</mo><mo>&#8202;</mo><mo>)</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>16</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>&#8242;</mo><mo>&#8745;</mo><mi>B</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>36</mn></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∩</mo><mi>B</mi><mo>)</mo><mo>=</mo><mi>x</mi></math>, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>A</mi><mo>'</mo><mo> </mo><menclose notation="left"><mo> </mo><mi>B</mi><mo>'</mo></menclose></mrow></mfenced></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> minutes, taken to complete a jigsaw puzzle can be modelled by a normal&nbsp;distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>6</mn></math>.</p>
<p>It is found that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>%</mo></math>&nbsp;of times taken to complete the jigsaw puzzle are longer than&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn><mo>.</mo><mn>8</mn></math>&nbsp;minutes.</p>
</div>

<div class="specification">
<p>Use&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><mn>32</mn><mo>.</mo><mn>29</mn></math> in the remainder of the question.</p>
</div>

<div class="specification">
<p>Six randomly chosen people complete the jigsaw puzzle.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By stating and solving an appropriate equation, show, correct to two decimal places,&nbsp;that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><mn>32</mn><mo>.</mo><mn>29</mn></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>86</mn></math>th percentile time to complete the jigsaw puzzle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly chosen person will take more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes to&nbsp;complete the jigsaw puzzle.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least five of them will take more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes to&nbsp;complete the jigsaw puzzle.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Having spent <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math> minutes attempting the jigsaw puzzle, a randomly chosen person had not&nbsp;yet completed the puzzle.</p>
<p>Find the probability that this person will take more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes to complete the&nbsp;jigsaw puzzle.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><strong>All answers in this question should be given to four significant figures.</strong></p>
<p><br>In a local weekly lottery, tickets cost <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>2</mn></math> each.</p>
<p>In the first week of the lottery, a player will receive <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mi>D</mi></math> for each ticket, with the probability&nbsp;distribution shown in the following table. For example, the probability of a player&nbsp;receiving <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>10</mn></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>03</mn></math>. The grand prize in the first week of the lottery is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>1000</mn></math>.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>If nobody wins the grand prize in the first week, the probabilities will remain the same, but the&nbsp;value of the grand prize will be <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>2000</mn></math> in the second week, and the value of the grand prize&nbsp;will continue to double each week until it is won. All other prize amounts will remain the same.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine whether this lottery is a fair game in the first week. Justify your answer.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the grand prize is not won and the grand prize continues to double, write an&nbsp;expression in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> for the value of the grand prize in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mtext>th</mtext></math>&nbsp;week of the lottery.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mtext>th</mtext></math> week is the first week in which the player is expected to make a profit. Ryan knows&nbsp;that if he buys a lottery ticket in the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mtext>th</mtext></math> week, his expected profit is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mi>p</mi></math>.</p>
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>On one day 180 flights arrived at a particular airport. The distance travelled and the arrival status for each incoming flight was recorded. The flight was then classified as on time, slightly delayed, or heavily delayed.</p>
<p>The results are shown in the following table.</p>
<p><img src="data:image/png;base64,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"></p>
<p>A <em>χ</em><sup>2</sup> test is carried out at the 10 % significance level to determine whether the arrival status of incoming flights is independent of the distance travelled.</p>
</div>

<div class="specification">
<p>The critical value for this test is 7.779.</p>
</div>

<div class="specification">
<p>A flight is chosen at random from the 180 recorded flights.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the alternative hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down&nbsp;the <em>χ</em><sup>2</sup> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down&nbsp;the associated <em>p</em>-value.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State, with a reason, whether you would reject the null hypothesis.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that this flight arrived on time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that this flight was not heavily delayed, find the probability that it travelled between 500 km and 5000 km.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two flights are chosen at random from those which were slightly delayed.</p>
<p>Find the probability that each of these flights travelled at least 5000 km.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>The flight times, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> minutes, between two cities can be modelled by a normal distribution with&nbsp;a mean of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>75</mn></math> minutes and a standard deviation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#963;</mi></math> minutes.</p>
</div>

<div class="specification">
<p>On a particular day, there are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>64</mn></math> flights scheduled between these two cities.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>%</mo></math> of the flight times are longer than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>82</mn></math> minutes, find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly selected flight will have a flight time of more than&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that a flight between the two cities takes longer than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> minutes, find the&nbsp;probability that it takes less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>82</mn></math> minutes.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected number of flights that will have a flight time of more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> minutes.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> of the flights on this particular day will have a flight&nbsp;time&nbsp;of more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80</mn></math> minutes.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the data collected from an experiment.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The data is also represented on the following scatter diagram.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAs0AAAF9CAYAAAD/bVVpAAAgAElEQVR4Ae29sY5tx5mlWe8xaHvUBAdtigKtLqBREKc9gYBktmiUgB6jy2jRK1kiegzRE4GSaIroKfV44kA0uh0RoC+CL0DxBcgnyMG6qv/W4Yncef4vzlmXGSdWAKmde++1V6y1/siM/24d3vs3DxlJIAkkgSSQBJJAEkgCSSAJPJnA3zx5NzeTQBJIAkkgCSSBJJAEkkASeEjTnEWQBJJAEkgCSSAJJIEkkAQuJJCm+UJAuZ0EkkASSAJJIAkkgSSQBNI0Zw0kgSSQBJJAEkgCSSAJJIELCaRpvhBQbieBJJAEkkASSAJJIAkkgcOm+d/8m//tIV/JIGsgayBrIGsgayBrIGsga2CHNXDpjwVPNs2XHs79JJAEkkASSAJJIAkkgSSwegL6Q8Glkab5UkK5nwSSQBJIAkkgCSSBJHDXCaRpvuvyxlwSSAJJIAkkgSSQBJLALRJI03yLFMORBJJAEkgCSSAJJIEkcNcJpGm+6/LGXBJIAkkgCSSBJJAEksAtEkjTfIsUw5EEkkASSAJJIAkkgSRw1wmkab7r8sZcEkgCSSAJJIEkkASSwC0SSNN8ixTDkQSSQBJIAkkgCSSBJHDXCaRpvuvyxlwSSAJJIAkkgSSQBJLALRJI03yLFMORBJJAEkgCSSAJJIEkcNcJpGm+6/LGXBJIAkkgCSSBJJAEksAtEkjTfIsUw3F1Al9++eWDFqO+fvazv3/J9957v/zW+csb+SYJJIEkkASSQBJIAq8wgTTNrzDsTHU5ATXMr7/+2kvgp5/+KU3zyzTyTRJIAkkgCSSBJPBdJZCm+btKPvM+msAHH/z6xdvmr7/++sX9jz763YO+MpJAEkgCSSAJJIEk8F0mkKb5u0w/cw8JqEHWotTHNdQ4v/vuzwdMXfjmm28ePvzwt3WaYxJIAkkgCSSBJJAEbAmkabZFG+KZBD7++A8vmmZ9LEOfZ1bzfDTeeeenL7C///0/H0FyPQkkgSSQBJJAEkgCN0kgTfNNYgzJrRL4/PM/v2iE9YZZDfTR+OSTPz689tr3XmB11FvnjCSQBJJAEkgCSSAJuBJI0+xKNrxTCdTfoqG3zEdDDfIbb3z/xUcztIDffvtHD3rrnJEEkkASSAJJIAkkAVcCaZpdyYZ3KgE1zU99jlmkv/jFPz783d/9hxf8WsBfffWXF2+dP/vss6k581ASSAJJIAkkgSSQBC4lkKb5UkK5b09A//HfW2/98MXfknH6dzQ/NrEaYy3aL7744sXtWsDvv/+rF2+f8zGNx1LLtSSQBJJAEkgCSeDaBKrneIrnb45udh4+ejbXk0AlUH/NnI6Xhj6GoQa5xuka1Nvn03uFyTEJJIEkkASSQBJIAtcmcNpzHHGlaT5KJtdfeQJ6w3z6Nvl0AetjGvrKSAJJIAkkgSSQBJLArRM47TmOuNM0HyWT6995Ap0F/J2LjIAkkASSQBJIAklg+QQ6PUea5uXLfL8GOgv4ft3HWRJIAkkgCSSBJPCqEuj0HGmaX1U1Mg9OoLOAMWkeSAJJIAkkgSSQBJLAWQKdniNN81loOX0+CXQW8PNRGyVJIAkkgSSQBJLAqgl0eo40zatWdwPdnQW8QQyxmASSQBJIAkkgCZgT6PQcaZrNRQj9fAKdBTzPnieTQBJIAkkgCSSBJPDXBDo9R5rmrJZnm0BnAT9b8RGWBJJAEkgCSSAJLJNAp+dI07xMOfcT2lnA+6USx0kgCSSBJJAEksCtE+j0HGmab516+G6WQGcB32yyECWBJJAEkkASSALbJtDpOdI0b7s8nr/xzgJ+/i6iMAkkgSSQBJJAEnjuCXR6jjTNz72KG+vrLOCN44n1JJAEkkASSAJJ4EYJdHqONM03Cjs0t0+gs4BvP2sYk0ASSAJJIAkkgd0S6PQcaZp3WxUL+e0s4IXsRGoSSAJJIAkkgSTwTBPo9Bxpmp9p8SLr4aGzgJNTEkgCSSAJJIEkkASuTaDTc6RpvjblPG9LoLOAbZOHOAkkgSSQBJJAEtgmgU7PkaZ5m+WwntHOAl7PVRQngSSQBJJAEkgCzy2BTs+Rpvm5VS16XibQWcAvwfkmCSSBJJAEkkASSAKTCXR6jjTNk+HmsTGB99775YvPIWvh/eQnP3748ssvB9AHH/z6JUY4nR+NzgI+ejbXk0ASSAJJIAkkgSTQTaDTc6Rp7qYZ3JMJqPmtBvjzz//88OabP3h4660fDs88dm0A/cuFzgI+ejbXk0ASSAJJIAkkgSTQTaDTc6Rp7qYZ3JMJ6C3z6ag3yp9++qeXl08b65cXn/ims4CfeDy3kkASSAJJIAkkgSTQSqDTc6RpbkUZEE1Ab5u1AE+bZr191jV9vfvuz1++mT7i7izgo2dzPQkkgSSQBJJAEkgC3QQ6PUea5m6awaEEPvrody8+onH+kD7nrLfS+syzFqia66PRWcBHz+Z6EkgCSSAJJIEkkAS6CXR6jjTN3TSDQwn87Gd//6DG+Wh8/fXXD6+//tqTb5s7C/iIP9eTQBJIAkkgCSSBJNBNoNNzpGnuphlcOwF9JENN86Wht83nn4U+fUYL+P/57//9xSUdn/r6X//zfz55v54Vmb4vfJ2f3z8/P8IX7vxY+PPrT51fq+X8+ZqLaDnCnnPXeeHrvOa8dF64p47FfY454i780f3iqftH+MKdHgt7eu2x74u77nXPi/8cXzznx8KfX3/svLDn3EfnXfxjc126VtznuGu11PNH/Ofz6fwIW1z1zOx58Z8/X7ynx8KeXnvs++IqfJ0X9uic4sWXkQR2SyBN824VfwZ+9Qa50zBLqhrmS01z15I2BTKeE55uUE7tTm7Vh3h1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbjyp6eg8V5LAmgmkaV6zbsuqJg2zTOpN8+l/KHhuvLOAz5/JeRJIAkkgCSSBJJAEaAKdniMfz6CpBn+YgP5GDDXOp+P0724+/Yyz3jAL/9ToLOB63v3mxclP3+o4tTi5VSvi1a2F8BMs9Sk85Sd4gp3RkpoqtXGQ3AlWM7nxpKaj81xJAmsm0Ok50jSvWdtnpVqNsv7REi24869qlD/++A8v7+mvnqtm+ikjnQVcz7s3ESc/3aCcWpzcqhXx6tZC+AmW+hSe8hM8wc5oSU2V2jhI7gSrmdx4UtPRea4kgTUT6PQcaZrXrO0WqjsLuIJwbyJOfrpBObU4uVUr4tWthfATLPUpPOUneIKd0ZKaKrVxkNwJVjO58aSmo/NcSQJrJtDpOdI0r1nbLVR3FvA9BLHTBrWL11186udvF6+7+Nyppvewf8TD7RLo9Bxpmm+Xd5hunEBnAdeU7jcvTn66GTu1OLlVK+LVrYXwEyz1KTzlJ3iCndGSmiq1cZDcCVYzufGkpqPzXEkCaybQ6TnSNK9Z2y1UdxZwBeHeRJz8dINyanFyq1bEq1sL4SdY6lN4yk/wBDujJTVVauMguROsZnLjSU1H57mSBNZMoNNzpGles7ZbqO4s4ArCvYk4+ekG5dTi5FatiFe3FsJPsNSn8JSf4Al2RktqqtTGQXInWM3kxpOajs5zJQmsmUCn50jTvGZtt1DdWcAVhHsTcfLTDcqpxcmtWhGvbi2En2CpT+EpP8ET7IyW1FSpjYPkTrCayY0nNR2d50oSWDOBTs+RpnnN2m6hWgu4Ngcd60vm63t6PH/21udET82tDUrP1XlxXHtePDPHa+c+er68zmiqZ464b3W/eGaOpa181nlxXXtePDPHa+c+f740lNc67xzPuW593tFwhDnSUj6P7hffpfuFmzle4qb3jzTIa0YS2C2BNM27VfzO/HYWcFnWL38ynhOeblBO7U5u1Yd4dWsh/ARLfQpP+QmeYGe0pKZKbRwkd4LVTG48qenoPFeSwJoJdHqOvGles7ZbqO4s4ArCvYk4+ekG5dTi5FatiFe3FsJPsNSn8JSf4Al2RktqqtTGQXInWM3kxpOajs5zJQmsmUCn50jTvGZtt1DdWcAVhHsTcfLTDcqpxcmtWhGvbi2En2CpT+EpP8ET7IyW1FSpjYPkTrCayY0nNR2d50oSWDOBTs+RpnnN2m6hurOAKwj3JuLkpxuUU4uTW7UiXt1aCD/BUp/CU36CJ9gZLampUhsHyZ1gNZMbT2o6Os+VJLBmAp2eI03zmrXdQnVnAVcQ7k3EyU83KKcWJ7dqRby6tRB+gqU+haf8BE+wM1pSU6U2DpI7wWomN57UdHSeK0lgzQQ6PUea5jVru4XqzgK+hyB22qB28bqLT/387eJ1F5/38Ds1HpLATAKdniNN80yyeeaVJNBZwCXE/ebFyU83Y6cWJ7dqRby6tRB+gqU+haf8BE+wM1pSU6U2DpI7wWomN57UdHSeK0lgzQQ6PUea5jVru4XqzgKuINybiJOfblBOLU5u1Yp4dWsh/ARLfQpP+QmeYGe0pKZKbRwkd4LVTG48qenoPFeSwJoJdHqONM1r1nYL1Z0FXEG4NxEnP92gnFqc3KoV8erWQvgJlvoUnvITPMHOaElNldo4SO4Eq5nceFLT0XmuJIE1E+j0HGma16ztFqo7C3iLIGIyCSSBJJAEkkASsCbQ6TnSNFtLEPJrEugs4OJ3v3lx8tO3Ok4tTm7Vinh1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbjyp6eg8V5LAmgl0eo40zWvWdgvVWsC1OehYXzJf39Pj+bO3Pid6am5tUHquzovj2vPimTleO/fR8+V1RlM9c8R9q/vFM3MsbeWzzovr2vPimTleO/f586WhvNZ553jOdevzjoYjzJGW8nl0v/gu3S/czPESN71/pEFeM5LAbgmkad6t4nfmt7OAy7J++ZPxnPB0g3Jqd3KrPsSrWwvhJ1jqU3jKT/AEO6MlNVVq4yC5E6xmcuNJTUfnuZIE1kyg03PkTfOatd1CdWcB30MQO21Qu3jdxad+/nbxuovPe/idGg9JYCaBTs+Rpnkm2TzzShLoLOAS4n7z4uSnm7FTi5NbtSJe3VoIP8FSn8JTfoIn2BktqalSGwfJnWA1kxtPajo6z5UksGYCnZ4jTfOatd1CdWcBVxDuTcTJTzcopxYnt2pFvLq1EH6CpT6Fp/wET7AzWlJTpTYOkjvBaiY3ntR0dJ4rSWDNBDo9R5rmNWu7herOAq4g3JuIk59uUE4tTm7Vinh1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbjyp6eg8V5LAmgl0eo40zWvWdgvVnQW8RRAxmQSSQBJIAkkgCVgT6PQcaZqtJQj5NQl0FnDxu9+8OPnpWx2nFie3akW8urUQfoKlPoWn/ARPsDNaUlOlNg6SO8FqJjee1HR0nitJYM0EOj1HmuY1a7uF6s4CriDcm4iTn25QTi1ObtWKeHVrIfwES30KT/kJnmBntKSmSm0cJHeC1UxuPKnp6DxXksCaCXR6jjTNa9Z2C9WdBVxBuDcRJz/doJxanNyqFfHq1kL4CZb6FJ7yEzzBzmhJTZXaOEjuBKuZ3HhS09F5riSBNRPo9Bxpmtes7RaqOwv4HoLYaYPaxesuPvXzt4vXXXzew+/UeEgCMwl0eo40zTPJ5plXkkBnAZcQ95sXJz/djJ1anNyqFfHq1kL4CZb6FJ7yEzzBzmhJTZXaOEjuBKuZ3HhS09F5riSBNRPo9Bxpmtes7RaqtYBrc9CxvmS+vqfH82dvfU701NzaoPRcnRfHtefFM3O8du6j58vrjKZ65oj7VveLZ+ZY2spnnRfXtefFM3O8du7z50tDea3zzvGc69bnHQ1HmCMt5fPofvFdul+4meMlbnr/SIO8ZiSB3RJI07xbxe/Mb2cBl2X98ifjOeHpBuXU7uRWfYhXtxbCT7DUp/CUn+AJdkZLaqrUxkFyJ1jN5MaTmo7OcyUJrJlAp+fIm+Y1a7uF6s4C3iKImEwCSSAJvMIE0jS/wrAz1bNJoNNzpGl+NuWKkPMEOgu4nnG/eXHy0w3KqcXJrVoRr24thJ9gqU/hKT/BE+yMltRUqY2D5E6wmsmNJzUdnedKElgzgU7PkaZ5zdpuobqzgCsI9ybi5KcblFOLk1u1Il7dWgg/wVKfwlN+gifYGS2pqVIbB8mdYDWTG09qOjrPlSSwZgKdniNN85q13UJ1ZwFXEO5NxMlPNyinFie3akW8urUQfoKlPoWn/ARPsDNaUlOlNg6SO8FqJjee1HR0nitJYM0EOj1HmuY1a7uF6s4CriDcm4iTn25QTi1ObtWKeHVrIfwES30KT/kJnmBntKSmSm0cJHeC1UxuPKnp6DxXksCaCXR6jjTNa9Z2C9WdBVxBuDcRJz/doJxanNyqFfHq1kL4CZb6FJ7yEzzBzmhJTZXaOEjuBKuZ3HhS09F5riSBNRPo9Bxpmtes7RaqOwu4gnBvIk5+ukE5tTi5VSvi1a2F8BMs9Sk85Sd4gp3RkpoqtXGQ3AlWM7nxpKaj81xJAmsm0Ok50jSvWdstVHcWcAXh3kSc/HSDcmpxcqtWxKtbC+EnWOpTeMpP8AQ7oyU1VWrjILkTrGZy40lNR+e5kgTWTKDTc6RpXrO2W6juLOAKwr2JOPnpBuXU4uRWrYhXtxbCT7DUp/CUn+AJdkZLaqrUxkFyJ1jN5MaTmo7OcyUJrJlAp+dI07xmbbdQrQVcm4OO9SXz9T09nj9763Oip+bWBqXn6rw4rj0vnpnjtXMfPV9eZzTVM0fct7pfPDPH0lY+67y4rj0vnpnjtXOfP18aymudd47nXLc+72g4whxpKZ9H94vv0v3CzRwvcdP7RxrkNSMJ7JZAmubdKn5nfjsLuCzrlz8ZzwlPNyindie36kO8urUQfoKlPoWn/ARPsDNaUlOlNg6SO8FqJjee1HR0nitJYM0EOj1H3jSvWdstVHcWcAXh3kSc/HSDcmpxcqtWxKtbC+EnWOpTeMpP8AQ7oyU1VWrjILkTrGZy40lNR+e5kgTWTKDTc6RpXrO2W6juLOAKwr2JOPnpBuXU4uRWrYhXtxbCT7DUp/CUn+AJdkZLaqrUxkFyJ1jN5MaTmo7OcyUJrJlAp+dI07xmbbdQ3VnAFYR7E3Hy0w3KqcXJrVoRr24thJ9gqU/hKT/BE+yMltRUqY2D5E6wmsmNJzUdnedKElgzgU7PkaZ5zdpuobqzgCsI9ybi5KcblFOLk1u1Il7dWgg/wVKfwlN+gifYGS2pqVIbB8mdYDWTG09qOjrPlSSwZgKdniNN85q13UJ1ZwHfQxA7bVC7eN3Fp37+dvG6i8+danoP+0c83C6BTs+Rpvl2eW/P9N57v3zQotPXT37y44cvv/xyyORnP/v7F/fffPMHDx9//Ifh/umFzgIuvPvNi5OfbsZOLU5u1Yp4dWsh/ARLfQpP+QmeYGe0pKZKbRwkd4LVTG48qenoPFeSwJoJdHqONM1r1vbZqf7gg18/6Evj88///KCm+K23fvgtne+++/MXzbQufvrpnx5ef/21RxvreqizgAvr3kSc/HSDcmpxcqtWxKtbC+EnWOpTeMpP8AQ7oyU1VWrjILkTrGZy40lNR+e5kgTWTKDTc6RpXrO2z0613jKfDjXQWoBqjjXUSJ+e65reOuvraHQWcD3r3kSc/HSDcmpxcqtWxKtbC+EnWOpTeMpP8AQ7oyU1VWrjILkTrGZy40lNR+e5kgTWTKDTc6RpXrO2z171eZOsJlpvlk/HY9dO73cW8Ck+3yeBJJAEkkASSAJJYCaBTs+Rpnkm2TxzMYGPPvrdi49oFFAfzdBHNk6HPtOsRfrYZ5+F6yzg4nO/eXHy07c6Ti1ObtWKeHVrIfwES30KT/kJnmBntKSmSm0cJHeC1UxuPKnp6DxXksCaCXR6jjTNa9b22avWxy7UONfQ+flnnKtp1lvpx4YWcP3y1rG+hK3v6fH82WvP6fxP4a/Vcv78U3PRe+fc157T+U/x18596fnTuej3l7jpfTr/U3g69yX8U3PRe5fmovfp/Kd4OhfFn85Fv6dznePJfHo2IwnslECa5p2q/Yy86nPM559V1pvm86ZZTbUWad40/3dUPedbJie3TGrT7g63FsJPsNSn8JSf4Al2Rktq+viKJrkT7EyNKD+p6ePuczUJrJdAmub1ara84q+//npomGXqsc8vP3btNIDOAi483RSeE55uUE7tTm7Vinh1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbvzoJleSwP0n0Ok58vGM+18Hr8zhUcMsAef/YaCu6e9yPn8jfSq2s4AL795EnPyk6ZBfpxYnt7QTr24thJ9gqc/UVAk8PmjuBE+wUkfWrvCEn2Ap9wyeetUcGUlg9QQ6PUea5tWr/Iz06yMYapxPh94m11CDrEZZQ59nzt/T/Ndk6Abl3GCd3HJLvLq1EH6CpT6Fp/wET7AzWlJTpTYOkjvBaiY3ntR0dJ4rSWDNBNI0r1m35VSrUdbnlbXgzr9O/2NAGVPTLEz+RcB/LTPdoJwbppNbjolXtxbCT7DUp/CUn+AJdkZLaqrUxkFyJ1jN5MaTmo7OcyUJrJlAmuY16xbV/5JAZwEnrCSQBJJAEkgCSSAJXJtAp+fIxzOuTTnP2xLoLOCa3P3mxclP3+o4tTi5VSvi1a2F8BMs9Sk85Sd4gp3RkpoqtXGQ3AlWM7nxpKaj81xJAmsm0Ok50jSvWdstVHcWcAXh3kSc/HSDcmpxcqtWxKtbC+EnWOpTeMpP8AQ7oyU1VWrjILkTrGZy40lNR+e5kgTWTKDTc6RpXrO2W6juLOAKwr2JOPnpBuXU4uRWrYhXtxbCT7DUp/CUn+AJdkZLaqrUxkFyJ1jN5MaTmo7OcyUJrJlAp+dI07xmbbdQ3VnA9xDEThvULl538amfv1287uLzHn6nxkMSmEmg03OkaZ5JNs+8kgQ6C7iEuN+8OPnpZuzU4uRWrYhXtxbCT7DUp/CUn+AJdkZLaqrUxkFyJ1jN5MaTmo7OcyUJrJlAp+dI07xmbbdQrQVcm4OO9SXz9T09nj9763Oip+bWBqXn6rw4rj0vnpnjtXMfPV9eZzTVM0fct7pfPDPH0lY+67y4rj0vnpnjtXOfP18aymudd47nXLc+72g4whxpKZ9H94vv0v3CzRwvcdP7RxrkNSMJ7JZAmubdKn5nfjsLuCzrlz8ZzwlPNyindie36kO8urUQfoKlPoWn/ARPsDNaUlOlNg6SO8FqJjee1HR0nitJYM0EOj1H3jSvWdstVHcW8BZBxGQSSAJJIAkkgSRgTaDTc6RptpYg5Nck0FnAxe9+8+Lkp291nFqc3KoV8erWQvgJlvoUnvITPMHOaElNldo4SO4Eq5nceFLT0XmuJIE1E+j0HGma16ztFqo7C7iCcG8iTn66QTm1OLlVK+LVrYXwEyz1KTzlJ3iCndGSmiq1cZDcCVYzufGkpqPzXEkCaybQ6TnSNK9Z2y1UdxZwBeHeRJz8dINyanFyq1bEq1sL4SdY6lN4yk/wBDujJTVVauMguROsZnLjSU1H57mSBNZMoNNzpGles7ZbqO4s4ArCvYk4+ekG5dTi5FatiFe3FsJPsNSn8JSf4Al2RktqqtTGQXInWM3kxpOajs5zJQmsmUCn50jTvGZtt1DdWcAVhHsTcfLTDcqpxcmtWhGvbi2En2CpT+EpP8ET7IyW1FSpjYPkTrCayY0nNR2d50oSWDOBTs+RpnnN2m6hurOAKwj3JuLkpxuUU4uTW7UiXt1aCD/BUp/CU36CJ9gZLampUhsHyZ1gNZMbT2o6Os+VJLBmAp2eI03zmrXdQnVnAVcQ7k3EyU83KKcWJ7dqRby6tRB+gqU+haf8BE+wM1pSU6U2DpI7wWomN57UdHSeK0lgzQQ6PUea5jVru4XqzgKuINybiJOfblBOLU5u1Yp4dWsh/ARLfQpP+QmeYGe0pKZKbRwkd4LVTG48qenoPFeSwJoJdHqONM1r1nYL1Z0FXEG4NxEnP92gnFqc3KoV8erWQvgJlvoUnvITPMHOaElNldo4SO4Eq5nceFLT0XmuJIE1E+j0HGma16ztFqq1gGtz0LG+ZL6+p8fzZ299TvTU3Nqg9FydF8e158Uzc7x27qPny+uMpnrmiPtW94tn5ljaymedF9e158Uzc7x27vPnS0N5rfPO8Zzr1ucdDUeYIy3l8+h+8V26X7iZ4yVuev9Ig7xmJIHdEkjTvFvF78xvZwGXZf3yJ+M54ekG5dTu5FZ9iFe3FsJPsNSn8JSf4Al2RktqqtTGQXInWM3kxpOajs5zJQmsmUCn58ib5jVru4XqzgKuINybiJOfblBOLU5u1Yp4dWsh/ARLfQpP+QmeYGe0pKZKbRwkd4LVTG48qenoPFeSwJoJdHqONM1r1nYL1Z0FXEG4NxEnP92gnFqc3KoV8erWQvgJlvoUnvITPMHOaElNldo4SO4Eq5nceFLT0XmuJIE1E+j0HGma16ztFqo7C7iCcG8iTn66QTm1OLlVK+LVrYXwEyz1KTzlJ3iCndGyY02/+uovD++//6sXX5999pliGwbJnWA1kRtPajoYz4UksGgCnZ4jTfOixd1BdmcBVw7uTcTJTzcopxYnt2pFvLq1EH6CpT6Fp/wET7AzWnar6Sef/PFBv5tOv37/+39WdN8aJHeC1SRuPKnpt0znJAksnECn50jTvHCB7116ZwFXBu5NxMlPNyinFie3akW8urUQfoKlPoWn/ARPsDNadqvpG298/1sNs35Pvfba9xTdtwbJnWA1iRtPavot0zlJAgsn0Ok50jQvXOB7l95ZwJWBexNx8tMNyqnFya1aEa9uLYSfYKlP4Sk/wRPsjJbdaqrfS499KbvTQXInWM3hxpOannrO90lg5QQ6PUea5pUrfOfaOwu4InBvIk5+ukE5tTi5VSvi1a2F8BMs9Sk85Sd4gp3RsltN86ZZqyQjCdxfAp2eI03z/dX9bhx1FvDdmK+UMpkAACAASURBVI2RJJAElkig+5nmJcwciCR/EDqgyOUksFwCnZ4jTfNyZd1HcGcBVxrut2lOfrpBObU4uVUr4tWthfATLPUpPOUneIKd0bJjTfO3Z2ilZCSB+0qg03Okab6vmt+VGy3g2vB1rC+ZrO/p8fzZW58TPTW3mg49V+fFce158cwcr5376PnyOqOpnjnivtX94pk5lrbyWefFde158cwcr537/PnSUF7rvHM857r1eUfDEeZIS/k8ul98l+4XbuZ4iZveP9IgrxlJYLcE0jTvVvE789tZwGVZv/zJeE54ukE5tTu5VR/i1a2F8BMs9Sk85Sd4gp3RkpoqtXGQ3AlWM7nxpKaj81xJAmsm0Ok58qZ5zdpuobqzgO8hiJ02qF287uJTP3+7eN3F5z38To2HJDCTQKfnSNM8k2yeeSUJdBZwCXG/eXHy083YqcXJrVoRr24thJ9gqU/hKT/BE+yMltRUqY2D5E6wmsmNJzUdnedKElgzgU7PkaZ5zdpuobqzgCsI9ybi5KcblFOLk1u1Il7dWgg/wVKfwlN+gifYGS2pqVIbB8mdYDWTG09qOjrPlSSwZgKdniNN85q13UJ1ZwFXEO5NxMlPNyinFie3akW8urUQfoKlPoWn/ARPsDNaUlOlNg6SO8FqJjee1HR0nitJYM0EOj1HmuY1a7uF6s4C3iKImEwCSSAJJIEkkASsCXR6jjTN1hKE/JoEOgu4+N1vXpz89K2OU4uTW7UiXt1aCD/BUp/CU36CJ9gZLampUhsHyZ1gNZMbT2o6Os+VJLBmAp2eI03zmrXdQnVnAVcQ7k3EyU83KKcWJ7dqRby6tRB+gqU+haf8BE+wM1pSU6U2DpI7wWomN57UdHSeK0lgzQQ6PUea5jVru4XqzgKuINybiJOfblBOLU5u1Yp4dWsh/ARLfQpP+QmeYGe0pKZKbRwkd4LVTG48qenoPFeSwJoJdHqONM1r1nYL1Z0FfA9B7LRB7eJ1F5/6+dvF6y4+7+F3ajwkgZkEOj1HmuaZZPPMK0mgs4BLiPvNi5OfbsZOLU5u1Yp4dWsh/ARLfQpP+QmeYGe0pKZKbRwkd4LVTG48qenoPFeSwJoJdHqONM1r1nYL1VrAtTnoWF8yX9/T4/mztz4nempubVB6rs6L49rz4pk5Xjv30fPldUZTPXPEfav7xTNzLG3ls86L69rz4pk5Xjv3+fOlobzWeed4znXr846GI8yRlvJ5dL/4Lt0v3MzxEje9f6RBXjOSwG4JpGnereJ35rezgMuyfvmT8ZzwdINyandyqz7Eq1sL4SdY6lN4yk/wBDujJTVVauMguROsZnLjSU1H57mSBNZMoNNz5E3zmrXdQnVnAW8RREwmgSSQBJJAEkgC1gQ6PUeaZmsJQn5NAp0FXPzuNy9OfvpWx6nFya1aEa9uLYSfYKlP4Sk/wRPsjJbUVKmNg+ROsJrJjSc1HZ3nShJYM4FOz5Gmec3abqG6s4ArCPcm4uSnG5RTi5NbtSJe3VoIP8FSn8JTfoIn2BktqalSGwfJnWA1kxtPajo6z5UksGYCnZ4jTfOatd1CdWcBVxDuTcTJTzcopxYnt2pFvLq1EH6CpT6Fp/wET7AzWlJTpTYOkjvBaiY3ntR0dJ4rSWDNBDo9R5rmNWv7bFW/994vH9588wcPH3/8h0c1fvDBrx+0MOtL50ejs4DrWfcm4uSnG5RTi5NbtSJe3VoIP8FSn8JTfoIn2BktqalSGwfJnWA1kxs/usmVJHD/CXR6jjTN978OXpnDd9/9+ctm+KhpfuutH7b1dBZwkbk3ESc/aTrk16nFyS3txKtbC+EnWOozNVUCjw+aO8ETrNSRtSs84SdYyj2Dp141R0YSWD2BTs+Rpnn1Kj8z/Z9//ucXjfNjTbPeKj/1ZvncSmcB1zPPbdMheugGRbiVD8ETLOUWnnh1ayH8BEt9zuRI9BDsjJbUVKmNg+ROsJrJjSc1HZ3nShJYM4FOz5Gmec3aPlvVTzXN+tiGFqW+9Fb6UgPdWcAVhHsTcfLTDcqpxcmtWhGvbi2En2CpT+EpP8ET7IyW1FSpjYPkTrCayY0nNR2d50oSWDOBTs+RpnnN2j5b1U81zRL95ZdfPuhzzz/5yY9fNM/CH43OAq5n3ZuIk59uUE4tTm7Vinh1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbjyp6eg8V5LAmgl0eo40zWvW9tmqvtQ0l/Cvv/764fXXX3vybXNnARefexNx8tMNyqnFya1aEa9uLYSfYKlP4Sk/wRPsjJbUVKmNg+ROsJrJjSc1HZ3nShJYM4FOz5Gmec3aPlvV3aZZBvS2WW+dj4YWcP3y1rG+hK/v6fH82WvP6fxP4a/Vcv78U3PRe+fc157T+U/x18596fnTuej3l7jpfTr/U3g69yX8U3PRe5fmovfp/Kd4OhfFn85Fv6dznePJfHo2IwnslECa5p2q/Uy8kqZZDfOlprlry/3mxcmvjYwMpxYntzwSr24thJ9gqU/hKT/BE+yMltRUqY2D5E6wmsmNJzUdnedKElgzgTTNa9ZtadWkadab5k8//dOh384CPnw4N5JAEkgCSWAqgTTNU7HlocUT6PQc+XjG4kV+bvLVBGvhffTR774lTc306TW9YdbfoPHU6Czget795sXJTzcopxYnt2pFvLq1EH6CpT6Fp/wET7AzWlJTpTYOkjvBaiY3ntR0dJ4rSWDNBDo9R5rmNWv7LFXrr5DToquv049e6O9truv6q+cu/XVzMthZwBWEexNx8tMNyqnFya1aEa9uLYSfYKlP4Sk/wRPsjJbUVKmNg+ROsJrJjSc1HZ3nShJYM4FOz5Gmec3abqG6s4ArCPcm4uSnG5RTi5NbtSJe3VoIP8FSn8JTfoIn2BktqalSGwfJnWA1kxtPajo6z5UksGYCnZ4jTfOatd1CdWcBVxDuTcTJTzcopxYnt2pFvLq1EH6CpT6Fp/wET7AzWlJTpTYOkjvBaiY3ntR0dJ4rSWDNBDo9R5rmNWu7herOAq4g3JuIk59uUE4tTm7Vinh1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbjyp6eg8V5LAmgl0eo40zWvWdgvVnQVcQbg3ESc/3aCcWpzcqhXx6tZC+AmW+hSe8hM8wc5oSU2V2jhI7gSrmdx4UtPRea4kgTUT6PQcaZrXrO0WqjsLuIJwbyJu/vLROTq1OLk73k4xbi2En2BPPXS/p/wET7DSS/FdjzPcVAvBEyzxWFjCT7CvIsc0zVXFHHdKoNNzpGneaUUs5rWzgMvSc9t0iB66QRFu5UPwBEu5hSde3VoIP8FSnzM5Ej0EO6MlNVVq4yC5E6xmcuNJTUfnuZIE1kyg03OkaV6ztluo1gKuzUHH+pL5+p4ez5+99TnRU3Nrg9JzdV4c154Xz8zx2rmPni+vM5rqmSPuW90vnpljaSufdV5c154Xz8zx2rnPny8N5bXOO8dzrlufdzQcYY60lM+j+8V36X7hZo6XuOn9Iw3ympEEdksgTfNuFb8zv50FXJb1y5+M54SnG5RTu5Nb9SFe3VoIP8FSn8JTfoIn2BktqalSGwfJnWA1kxtPajo6z5UksGYCnZ4jb5rXrO0WqjsL+B6C2GmD2sXrLj7187eL11183sPv1HhIAjMJdHqONM0zyeaZV5JAZwGXEPebFyc/3YydWpzcqhXx6tZC+AmW+hSe8hM8wc5oSU2V2jhI7gSrmdx4UtPRea4kgTUT6PQcaZrXrO0WqjsLuIJwbyJOfrpBObU4uVUr4tWthfATLPUpPOUneIKd0ZKaKrVxkNwJVjO58aSmo/NcSQJrJtDpOdI0r1nbLVR3FnAF4d5EnPx0g3JqcXKrVsSrWwvhJ1jqU3jKT/AEO6MlNVVq4yC5E6xmcuNJTUfnuZIE1kyg03OkaV6ztluo7izgLYKIySSQBJJAEkgCScCaQKfnSNNsLUHIr0mgs4CL3/3mxclP3+o4tTi5VSvi1a2F8BMs9Sk85Sd4gp3R4qjpZ5999vDFF188q1yIT5qju0aUn3qV34wksHoCnZ4jTfPqVb5j/Z0FXPbppvCc8HSDcmp3cqtWxKtbC+EnWOpTeMpP8AQ7o+WWNVWj/MYb33/Qz76+/vZv//3DV1/9RbJag3glWE1OfApP+AmWcs/gqVfNkZEEVk+g03OkaV69ynesv7OAy/5z23SIHrpBEW7lQ/AES7mFJ17dWgg/wVKfMzkSPQQ7o+WWNX377R+9bJircda17iBeCVbzE580R6rFjadeu/UJLgk85wQ6PUea5udcwc21dRbw5hHFfhJ4ZQl8+OFvX74Ffuedn6I3wF2R1SifH7vPB5cEkkASmE2g03OkaZ5NN8/ZE+gs4BLhfvPi5KdvdZxanNyqFfHq1kL4CZb6FJ7yEzzBHmn5/e//eXgDrI9RUK+XtJw3y3X+YqLG/1ziP6UgWOpTeMJPsJR7Bk9+TsWfkQTuIYFOz5Gm+R4qfacetIBrM9GxvmS3vqfH82dvfU701NzaoPRcnRfHtefFM3O8du6j58vrjKZ65oj7VveLZ+ZY2spnnRfXtefFM3O8Zu7/+B//z6Fp1s/nb37zTy/+IET1HGn5v/7zfx7m0bUjfM17fr+uzxzPuer8VjWd0VTPlJZbnRfP+VFeM5LAbgmkad6t4nfmt7OAy7J+6ZPxnPB0g3Jqd3KrPsSrWwvhJ1jqU3jKT/AEe6Tlsc8a6+dTf8vFrWv6/vu/evExEL3J/vl//a+S1B7EK8FKAPEpPOEnWMo9g6deNUdGElg9gU7PkTfNq1f5jvV3FvAd24+1JPBsElAjq5/H06/XXvvewzfffPNsNEZIEkgCSeCaBDo9R5rmaxLOs9YEOgu4BDy3NzVED32rQ7iVD8ETLOUWnnh1ayH8BEt9zuRI9BDsU1p+8Yt/fNk0q2HWXw9Hvd5Ky4uJH/kfwk+w1KfwhJ9gKfcMnvycij8jCdxDAp2eI03zPVT6Tj10FnBZf26bDtFDNyjCrXwInmApt/DEq1sL4SdY6nMmR6KHYC9p0ZvlapaF1UhN/yWIswPJnWA1jRtPanpmO6dJYNkEOj1HmuZly3v/wjsLuFJwbyJOfrpBObU4uVUr4tWthfATLPUpPOUneIKd0ZKaKrVxkNwJVjO58aSmo/NcSQJrJtDpOdI0r1nbLVR3FvAWQcRkEkgCSSAJJIEkYE2g03OkabaWIOTXJNBZwMXvfvPi5KdvdZxanNyqFfHq1kL4CZb6FJ7yEzzBzmhJTZXaOEjuBKuZ3HhS09F5riSBNRPo9Bxpmtes7RaqOwu4gnBvIk5+ukE5tTi5VSvi1a2F8BMs9Sk85Sd4gp3RkpoqtXGQ3AlWM7nxpKaj81xJAmsm0Ok50jSvWdstVHcWcAXh3kSc/HSDcmpxcqtWxKtbC+EnWOpTeMpP8AQ7oyU1VWrjILkTrGZy40lNR+e5kgTWTKDTc6RpXrO2W6juLOB7CGKnDWoXr7v41M/fLl538XkPv1PjIQnMJNDpOdI0zySbZ15JAp0FXELcb16c/HQzdmpxcqtWxKtbC+EnWOpTeMpP8AQ7oyU1VWrjILkTrGZy40lNR+e5kgTWTKDTc6RpXrO2W6jWAq7NQcf6kvn6nh7Pn731OdFTc2uD0nN1XhzXnhfPzPHauY+eL68zmuqZI+5b3S+emWNpK591XlzXnhfPzPHauc+fLw3ltc47x3OuW593NBxhjrSUz6P7xXfpfuFmjpe46f0jDfKakQR2SyBN824VvzO/nQVclvXLn4znhKcblFO7k1v1IV7dWk75P/nkjw9vvPH9F//inf61O/2z0afjFHt6/eh74lMclJ/gCXZGC/Hq1kL4CVa5EJ80R6rFjade5TcjCayeQKfnyJvm1at8x/o7C7jsuzcRN3/56BydWpzcHW+nGLeW4v/qq788qFHWejv9UiNdo7B1fusj5Sd4gpUviidZUG4nnnITnzRHqsWNT9NMqx38PSTQ6TnSNN9Dpe/UQ2cBl3X3JuLkpxuUU4uTW7UiXt1aiv/DD3/7rWa5Gud33vlpLS/cSBKfmqS0vJzwwjcET7AzWohXtxbCT7DKhfikOVItbjz1emG55nYSWCKBTs+RpnmJUu4psrOAKxn3JuLkpxuUU4uTW7UiXt1aij9Nc/0U/fVYuXz76vHZc6zpsdp/veP0qVkIP8FS7hk8qem/JprvksDaCXR6jjTNa9f4rtV3FnAF8Nw2HaKHblCEW/kQPMFSbuGJV7eW4nd8PIP4nMmxtOvZS4NgxUXxxCvlduIpN/FJc6Ra3Hjq9dIazP0ksEICnZ4jTfMKldxUY2cBVzTuTcTJTzcopxYnt2pFvLq1nPJ/8cUX3/oPAX//+3+upfXieIr91o2DE+JTFJSf4Al2Rgvx6tZC+AlWuRCfNEeqxY2nXuU3IwmsnkCn50jTvHqV71h/ZwGXffcm4uSnG5RTi5NbtSJe3VoIP8FSn8JTfoIn2BktqalSGwfJnWA1kxtPajo6z5UksGYCnZ4jTfOatd1CdWcBVxDuTcTJTzcopxYnt2pFvLq1EH6CpT6Fp/wET7AzWlJTpTYOkjvBaiY3ntR0dJ4rSWDNBDo9R5rmNWu7herOAq4g3JuIm798dI5OLU7ujrdTjFsL4SfYUw/d7yk/wROs9FJ81+MMN9VC8ARLPBaW8BPsq8gxTXNVMcedEuj0HGmad1oRi3ntLOCy9Nw2HaKHblCEW/kQPMFSbuGJV7cWwk+w1OdMjkQPwc5oSU2V2jhI7gSrmdx4UtPRea4kgTUT6PQcaZrXrO0WqrWAa3PQsb5kvr6nx/Nnb31O9NTc2qD0XJ0Xx7XnxTNzvHbuo+fL64ymeuaI+1b3i2fmWNrKZ50X17XnxTNzvHbu8+dLQ3mt887xnOvW5x0NR5gjLeXz6H7xXbpfuJnjJW56/0iDvGYkgd0SSNO8W8XvzG9nAZdl/fIn4znh6Qbl1O7kVn2IV7cWwk+w1KfwlJ/gCXZGS2qq1MZBcidYzeTGk5qOznMlCayZQKfnyJvmNWu7herOAr6HIHbaoHbxuotP/fzt4nUXnzvV9B72j3i4XQKdniNN8+3yDtONE+gs4JrS/ebFyU83Y6cWJ7dqRby6tRB+gqU+haf8BE+wM1pSU6U2DpI7wWomN57UdHSeK0lgzQQ6PUea5jVru4XqzgKuINybiJOfblBOLU5u1Yp4dWsh/ARLfQpP+QmeYGe0pKZKbRwkd4LVTG48qenoPFeSwJoJdHqONM1r1nYL1Z0FXEG4NxEnP92gnFqc3KoV8erWQvgJlvoUnvJfwutfNHz77R89vPPOTx9+85t/qh+T1vES9zlJanqeyF/PSY4EK3Y3ntT0cfe5mgTWS6DTc6RpXq+u2yjuLOBtwojRJNBM4Be/+McH/eycfn3yyR+bTweWBJJAEtgzgU7PkaZ5z7Vhc/3ee798ePPNHzx8/PEfHp3jZz/7+xeb+VOYerCzgAvrfvPi5KdvdZxanNyqFfHq1kL4CZb6FJ7yP4U/bZbr+zfe+H79qFw8PsX92MOp6WOpsJrSzN14UtPH3edqElgvgU7PkaZ5vbo+W8Xvvvvzl2+3Hmuadf8nP/nxC/2ffvqnh9dff+3hyy+/PPTTWcD1sHsTcfLTDcqpxcmtWhGvbi2En2CpT+Ep/xH+s88+e/kzWA1zHetn5dLxiPvoudT08WRIjgSr2dx4UtPH3edqElgvgU7PkaZ5vbo+a8Wff/7nF5v2edNc19Us19BbZ30djc4Crmfdm4iTn25QTi1ObtWKeHVrIfwES30KT/mfwr/22veGxlmfb+6Op7gf40hNH0uF1ZRm7saTmj7uPleTwHoJdHqONM3r1fVZK67m+Lxp/uCDX794s3wq/rFrp/c7C/gUn++TQBJ4eNB/BKifnfr6d//u/3j44osvEk0SSAJJIAk8kUCn50jT/ESAucUTOGqa9dEMfY75dKix1iI9+ohGZwEXn/vNi5OfvtVxanFyq1bEq1sL4SdY6lN4yn8J/9VXf3nRPKuB/v8+/rh+TFrHS9znJKnpeSJ/PSc5EqzY3XhS08fd52oSWC+BTs+Rpnm9uj5rxUdNsz6G8dZbP/yW9mqa9cxjQwu4fnnrWF/C1vf0eP7sted0/qfw12o5f/6puei9c+5rz+n8p/hr5770/Olc9PtL3PQ+nf8pPJ37Ev6puei9S3PR+3T+Uzydi+JP56Lf07nO8WQ+PZuRBHZKIE3zTtV+Jl6Pmma9aT5vmj/66Hd50wzfvqrMzrdMTm5p16bdHW4thJ9gqU/hKT/BE+yMltT08RVNcifYmRpRflLTx93nahJYL4E0zevVbHnFR03zY59ffuzaaQCdBVx4uik8JzzdoJzandyqFfHq1kL4CZb6FJ7yEzzBzmhJTZXaOEjuBKuZ3PjRTa4kgftPoNNz5OMZ978OXqnDo6a5rp/+7Rn66+fyt2ewRlLFdG6YTm5pT4P1+I+jM3cnd2r6eD11leROsJR7Bk9+To8TyJ0ksFYCaZrXqtddqFVTrIWnj16cDzXI9fc06/PM+Xua/5oQ3aCcG6yTW26JV7cWwk+w1KfwlJ/gCXZGS2qq1MZBcidYzeTGk5qOznMlCayZQJrmNeu2rGp93EKLrr70rwOeDzXNup9/EfBfk6EblHPDdHLLMfHq1kL4CZb6FJ7yEzzBzmhJTZXaOEjuBKuZ3HhS09F5riSBNRNI07xm3aL6XxLoLOCElQSSQBJIAkkgCSSBaxPo9Bz5TPO1Ked5WwKdBVyTu9+8OPnpWx2nFie3akW8urUQfoKlPoWn/ARPsDNaUlOlNg6SO8FqJjee1HR0nitJYM0EOj1HmuY1a7uF6s4CriDcm4iTn25QTi1ObtWKeHVrIfwES30KT/kJnmBntKSmSm0cJHeC1UxuPKnp6DxXksCaCXR6jjTNa9Z2C9WdBVxBuDcRJz/doJxanNyqFfHq1kL4CZb6FJ7yEzzBzmhJTZXaOEjuBKuZ3HhS09F5riSBNRPo9Bxpmtes7RaqOwv4HoLYaYPaxesuPvXzt4vXXXzew+/UeEgCMwl0eo40zTPJ5plXkkBnAZcQ95sXJz/djJ1anNyqFfHq1kL4CZb6FJ7yEzzBzmhJTZXaOEjuBKuZ3HhS09F5riSBNRPo9Bxpmtes7RaqtYBrc9CxvmS+vqfH82dvfU701NzaoPRcnRfHtefFM3O8du6j58vrjKZ65oj7VveLZ+ZY2spnnRfXtefFM3O8du7z50tDea3zzvGc69bnHQ1HmCMt5fPofvFdul+4meMlbnr/SIO8ZiSB3RJI07xbxe/Mb2cBl2X98ifjOeHpBuXU7uRWfYhXtxbCT7DUp/CUn+AJdkZLaqrUxkFyJ1jN5MaTmo7OcyUJrJlAp+fIm+Y1a7uF6s4C3iKImEwCSSAJvMIE0jS/wrAz1bNJoNNzpGl+NuWKkPMEOgu4nnG/eXHy0w3KqcXJrVoRr10tH37424e33/7Rw0//0396+Oyzz2pJXDx2+UVEsNTnDD/RQ7AzWhw1lQ4Np3bKTXxS7VSLG0+9/rVa+d8ksHYCnZ4jTfPaNb5r9Z0FXAG4NxEnP92gnFqc3KoV8drR8g//8F9e/rPtWi/6+uSTP9ayePLY4S8CgqU+haf8BE+wM1puXdPKfEYL8Uqw0kJ8Uu1UixtPvZ7WLN8ngVUT6PQcaZpXre4GujsLuGJwbyJOfrpBObU4uVUr4vWSlq+++svQMGvN6K1zZ1ziP+UgWOpTeMpP8AQ7o+WWNT3NfEYL8Uqw0kJ8Uu1UixtPvZ7XLedJYMUEOj1HmuYVK7uJ5s4Crijcm4iTn25QTi1ObtWKeL2kRR/F0Bo5/3rjje/XsnjyeIn/9GGCpT6Fp/wET7AzWm5Z09PMZ7QQrwQrLcQn1U61uPHU63ndcp4EVkyg03OkaV6xspto7izgisK9iTj56QbV0aKPKKh5VIZ/+7f//uGLL76oqJ48drhPCSieeL3E/c033zy89tr3hqb5nXd+eirx8PtL/KcPEqyeIz6Fp/wET7AzWohXtxbCT7DumlItbjypqbLJSAL3kECn50jTfA+VvlMPnQVc1t2biJOfblCXtDz2BlbNpT7OcGlc4j5/nuKJ1w7373//z99qmrs+5aPDX34JVs8Qn1QLxVPtFE+8Um4nnnITn8+tRm6v8puRBFZPoNNzpGlevcp3rL+zgMs+3RSeE/7Wm/H77//qW42kctSX/paJS8OdC/Ha1aI/DMjb//3f/tuD3j53R5dffAQrPPE5w0/0EOyMFuLVrYXwE6y7plSLG09qqmwyksA9JNDpOdI030Ol79RDZwGXdfcm4uSnG9QlLUdNs65fGpe4z5+neOKVcjvxlJv4VKaUn+AJdkYL8erWQvgJVrkQnzRHqsWNp17lNyMJrJ5Ap+dI07x6le9YvxZwbQ461pcs1/f0eP7src+JnppbG5Seq/PimD3/zW/+6dE3zf/v//gf7dxm576kvbwWbubo0jaj5fyZ0lY+67xw154Xz8zx2rnPny8N5bXOO8dzrlufdzQcYY60lM+j+8V36X7hZo6XuOn9Iw3ympEEdksgTfNuFb8zv50FXJb1y5+M54SnG1RHu94q138k92//7f/+oM/+dkaH+5SH4olXyu3EU27iU3lSfoIn2BktxKtbC+EnWOVCfNIcqRY3nnqV34wksHoCnZ4jb5pXr/Id6+8s4LLv3kSc/HSDcmpxcqtWxKtbC+EnWOpTeMpP8AQ7oyU1VWrjILkTrGZy40lNR+e5kgTWTKDTc6RpXrO2W6juLOAKwr2JOPnpBuXU4uRWrYhXtxbCT7DUp/CUn+AJdkZLaqrUxkFyJ1jN5MaTmo7OcyUJrJlAp+dI07xmbbdQ3VnAFYR7E3Hy0w3KqcXJrVoRr24thJ9gqU/heWAgsgAAH99JREFUKT/BE+yMltRUqY2D5E6wmsmNJzUdnedKElgzgU7PkaZ5zdpuobqzgCsI9ybi5KcblFOLk1u1Il7dWgg/wVKfwlN+gifYGS2pqVIbB8mdYDWTG09qOjrPlSSwZgKdniNN85q13UJ1ZwFXEO5NxMlPNyinFie3akW8urUQfoKlPoWn/ARPsDNaUlOlNg6SO8FqJjee1HR0nitJYM0EOj1HmuY1a7uF6s4CriDcm4iTn25QTi1ObtWKeHVrIfwES30KT/kJnmBntKSmSm0cJHeC1UxuPKnp6DxXksCaCXR6jjTNa9Z2C9WdBVxBuDcRJz/doJxanNyqFfHq1kL4CZb6FJ7yEzzBzmhJTZXaOEjuBKuZ3HhS09F5riSBNRPo9Bxpmtes7RaqOwu4gnBvIk5+ukE5tTi5VSvi1a2F8BMs9Sk85Sd4gp3RkpoqtXGQ3AlWM7nxpKaj81xJAmsm0Ok50jSvWdstVHcW8BZBxGQSSAJJIAkkgSRgTaDTc6RptpYg5Nck0FnAxe9+8+Lkp291nFqc3KoV8erWQvgJlvoUnvITPMHOaElNldo4SO4Eq5nceFLT0XmuJIE1E+j0HGma16ztFqq1gGtz0LG+ZL6+p8fzZ299TvTU3Nqg9FydF8e158Uzc7x27qPny+uMpnrmiPtW94tn5ljaymedF9e158Uzc7x27vPnS0N5rfPO8Zzr1ucdDUeYIy3l8+h+8V26X7iZ4yVuev9Ig7xmJIHdEkjTvFvF78xvZwGXZf3yJ+M54ekG5dTu5FZ9iFe3FsJPsNSn8JSf4Al2RktqqtTGQXInWM3kxpOajs5zJQmsmUCn58ib5jVru4XqzgK+hyB22qB28bqLT/387eJ1F5/38Ds1HpLATAKdniNN80yyeeaVJNBZwCXE/ebFyU83Y6cWJ7dqRby6tRB+gqU+haf8BE+wM1pSU6U2DpI7wWomN57UdHSeK0lgzQQ6PUea5jVru4XqzgKuINybiJOfblBOLU5u1Yp4dWsh/ARLfQpP+QmeYGe0pKZKbRwkd4LVTG48qenoPFeSwJoJdHqONM1r1nYL1Z0FXEG4N5Hi/+qrvzy8//6vXnz9/vf/XNMPx8IPNx65QDcowq3pCJ5gKbfwxKtbC+EnWOpzJkeih2BntKSmSm0cJHeC1UxuPKnp6DxXksCaCXR6jjTNa9Z2C9WdBfwqg/jiiy8eXnvtew/SVV//8A//5VVKyFxJIAkkgSSQBJKAIYFOz5Gm2RB8KG+TQGcB10zuNy/if+edn75slqtp1lFvn88H0UPf6hBu6SJ4gqXcwhOvbi2En2Cpz5kciR6CndGSmiq1cZDcCVYzufGkpqPzXEkCaybQ6TnSNK9Z2y1UdxZwBeHeRMT/9ts/erRp/uyzz0rGyyPRQzcowi1BBE+wlFt44tWthfATLPU5kyPRQ7AzWlJTpTYOkjvBaiY3ntR0dJ4rSWDNBDo9R5rmNWu7herOAq4g3JuI+POmudL+1yPNnWzGlNuJp9zEp9Kk/ARPsDNaiFe3FsJPsMqF+KQ5Ui1uPPUqvxlJYPUEOj1HmubVq3zH+jsL+FXaf+wzzR9++NurJey0Qe3idRefWvy7eN3F59W/0EKQBBZNoNNzpGletLg7yO4s4MrB/eal+L/55psHNcr6GzQe+1jGjB66GZeWmuvSkeAJVvNSPPFKuZ14yk18zuRI9BDsjBbi1a2F8BOsciE+aY5UixtPvcpvRhJYPYFOz5GmefUq37F+LeDaHHSsL1mu7+nx/NlbnxM9Nbc2KD1X58Vx7XnxzByvnfvo+fI6o6meOeK+1f3imTmWtvJZ58V17XnxzByvnfv8+dJQXuu8czznuvV5R8MR5khL+Ty6X3yX7hdu5niJm94/0iCvGUlgtwTSNO9W8Tvz21nAZVm//Ml4Tni6QTm1O7lVH+LVrYXwEyz1KTzlJ3iCndGSmiq1cZDcCVYzufGkpqPzXEkCaybQ6TnypnnN2m6hurOAKwj3JuLmLx+do1OLk7vj7RTj1kL4CfbUQ/d7yk/wBCu9FN/1OMNNtRA8wRKPhSX8BPsqciwPOSaBnRLo9BxpmndaEYt57SzgsvTcNh2ih77VIdzKh+AJlnILT7y6tRB+gqU+Z3Ikegh2RktqqtTGQXInWM3kxpOajs5zJQmsmUCn50jTvGZtt1DdWcAVhHsTcfLTDcqpxcmtWhGvbi2En2CpT+EpP8ET7IyW1FSpjYPkTrCayY0nNR2d50oSWDOBTs+RpnnN2m6hurOAKwj3JuLkpxuUU4uTW7UiXt1aCD/BUp/CU36CJ9gZLampUhsHyZ1gNZMbT2o6Os+VJLBmAp2eI03zmrXdQnVnAVcQ7k3EyU83KKcWJ7dqRby6tRB+gqU+haf8BE+wM1pSU6U2DpI7wWomN57UdHSeK0lgzQQ6PUea5jVru6zqDz749bf+KWqdH43OAq5n3ZuIk59uUE4tTm7Vinh1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbjyp6eg8V5LAmgl0eo40zWvWdlnVb731w7b2zgIuMvcm4uSnG5RTi5NbtSJe3VoIP8FSn8JTfoIn2BktqalSGwfJnWA1kxtPajo6z5UksGYCnZ4jTfOatV1Std4qP/Vm+dxUZwGfP7Pi+U4b1C5ed/Gpn7ddvO7ic6earrhfRLMvgU7PkabZl3+YzxJ4880fvPxoxrvv/vxiA91ZwDWF+82Lk59uxk4tTm7Vinh1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbjyp6eg8V5LAmgl0eo40zWvWdlnVX3755cN77/3y4Sc/+fGLBvrzz/986KWzgOth9ybi5KcblFOLk1u1Il7dWgg/wVKfwlN+gifYGS2pqVIbB8mdYDWTG09qOjrPlSSwZgKdniNN85q1XV71119//fD66689+bZZC7h+eetYXzJf39Pj+bPXntP5n8Jfq+X8+afmovfOua89p/Of4q+d+9Lzp3PR7y9x0/t0/qfwdO5L+KfmovcuzUXv0/lP8XQuij+di35P5zrHk/n0bEYS2CmBNM07VXtBr3rbrLfOR6OzgOtZ95sXJ782MjKcWpzc8ki8urUQfoKlPoWn/ARPsDNaUlOlNg6SO8FqJjee1HR0nitJYM0EOj1H3jSvWdu7UK2G+VZN88qB7LRB7eJ1F5/6udvF6y4+d6rpyvtGtN8+gTTNt880jDdMQG+aP/30T4eMnQVcD7vfvDj56Wbs1OLkVq2IV7cWwk+w1KfwlJ/gCXZGS2qq1MZBcidYzeTGk5qOznMlCayZQKfnyJvmNWu7nGr9B38fffS7l7r1hll/g8ZTo7OA63n3JuLkpxuUU4uTW7UiXt1aCD/BUp/CU36CJ9gZLampUhsHyZ1gNZMbT2o6Os+VJLBmAp2eI03zmrVdTvXHH//h5V83p796rvP3NXcWcAXh3kSc/HSDcmpxcqtWxKtbC+EnWOpTeMpP8AQ7oyU1VWrjILkTrGZy40lNR+e5kgTWTKDTc6RpXrO2W6juLOAKwr2JOPnpBuXU4uRWrYhXtxbCT7DUp/CUn+AJdkZLaqrUxkFyJ1jN5MaTmo7OcyUJrJlAp+dI07xmbbdQ3VnAFYR7E3Hy0w3KqcXJrVoRr24thJ9gqU/hKT/BE+yMltRUqY2D5E6wmsmNJzUdnedKElgzgU7PkaZ5zdpuobqzgCsI9ybi5KcblFOLk1u1Il7dWgg/wVKfwlN+gifYGS2pqVIbB8mdYDWTG09qOjrPlSSwZgKdniNN85q13UJ1ZwFXEO5NxM1fPjpHpxYnd8fbKcathfAT7KmH7veUn+AJVnopvutxhptqIXiCJR4LS/gJ9lXkmKa5qpjjTgl0eo40zTutiMW8dhZwWXpumw7RQzcowq18CJ5gKbfwxKtbC+EnWOpzJkeih2BntKSmSm0cJHeC1UxuPKnp6DxXksCaCXR6jjTNa9Z2C9VawLU56FhfMl/f0+P5s7c+J3pqbm1Qeq7Oi+Pa8+KZOV4799Hz5XVGUz1zxH2r+8Uzcyxt5bPOi+va8+KZOV479/nzpaG81nnneM516/OOhiPMkZbyeXS/+C7dL9zM8RI3vX+kQV4zksBuCaRp3q3id+a3s4DLsn75k/Gc8HSDcmp3cqs+xKtbC+EnWOpTeMpP8AQ7oyU1VWrjILkTrGZy40lNR+e5kgTWTKDTc+RN85q13UJ1ZwHfQxA7bVC7eN3Fp37+dvG6i897+J0aD0lgJoFOz5GmeSbZPPNKEugs4BLifvPi5KebsVOLk1u1Il7dWgg/wVKfwlN+gifYGS2pqVIbB8mdYDWTG09qOjrPlSSwZgKdniNN85q13UJ1ZwFXEO5NxMlPNyinFie3akW8urUQfoKlPoWn/ARPsDNaUlOlNg6SO8FqJjee1HR0nitJYM0EOj1HmuY1a7uF6s4CriDcm4iTn25QTi1ObtWKeHVrIfwES30KT/kJnmBntKSmSm0cJHeC1UxuPKnp6DxXksCaCXR6jjTNa9Z2C9WdBbxFEDGZBJJAEkgCSSAJWBPo9Bxpmq0lCPk1CXQWcPG737w4+elbHacWJ7dqRby6tRB+gqU+haf8BE+wM1pSU6U2DpI7wWomN57UdHSeK0lgzQQ6PUea5jVru4XqzgKuINybiJOfblBOLU5u1Yp4dWsh/ARLfQpP+QmeYGe0pKZKbRwkd4LVTG48qenoPFeSwJoJdHqONM1r1nYL1Z0FXEG4NxEnP92gnFqc3KoV8erWQvgJlvoUnvITPMHOaElNldo4SO4Eq5nceFLT0XmuJIE1E+j0HGma16ztFqo7C/gegthpg9rF6y4+9fO3i9ddfN7D79R4SAIzCXR6jjTNM8nmmVeSQGcBlxD3mxcnP92MnVqc3KoV8erWQvgJlvoUnvITPMHOaElNldo4SO4Eq5nceFLT0XmuJIE1E+j0HGma16ztFqq1gGtz0LG+ZL6+p8fzZ299TvTU3Nqg9FydF8e158Uzc7x27qPny+uMpnrmiPtW94tn5ljaymedF9e158Uzc7x27vPnS0N5rfPO8Zzr1ucdDUeYIy3l8+h+8V26X7iZ4yVuev9Ig7xmJIHdEkjTvFvF78xvZwGXZf3yJ+M54ekG5dTu5FZ9iFe3FsJPsNSn8JSf4Al2RktqqtTGQXInWM3kxpOajs5zJQmsmUCn58ib5jVru4XqzgLeIoiYTAJJIAkkgSSQBKwJdHqONM3WEoT8mgQ6C7j43W9enPz0rY5Ti5NbtSJe3VoIP8FSn8JTfoIn2BktqalSGwfJnWA1kxtPajo6z5UksGYCnZ4jTfOatd1CdWcBVxDuTcTJTzcopxYnt2pFvLq1EH6CpT6Fp/wET7AzWlJTpTYOkjvBaiY3ntR0dJ4rSWDNBDo9R5rmNWu7herOAq4g3JuIk59uUE4tTm7Vinh1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbjyp6eg8V5LAmgl0eo40zWvWdgvVnQV8D0HstEHt4nUXn/r528XrLj7v4XdqPCSBmQQ6PUea5plk88wrSaCzgEuI+82Lk59uxk4tTm7Vinh1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbjyp6eg8V5LAmgl0eo40zWvWdgvVnQVcQbg3ESc/3aCcWpzcqhXx6tZC+AmW+hSe8hM8wc5oSU2V2jhI7gSrmdx4UtPRea4kgTUT6PQcaZrXrO0WqjsLuIJwbyJOfrpBObU4uVUr4tWthfATLPUpPOUneIKd0ZKaKrVxkNwJVjO58aSmo/NcSQJrJtDpOdI0r1nbLVR3FnAF4d5EnPx0g3JqcXKrVsSrWwvhJ1jqU3jKT/AEO6MlNVVq4yC5E6xmcuNJTUfnuZIE1kyg03OkaV6ztluo7izgCsK9iTj56Qbl1OLkVq2IV7cWwk+w1KfwlJ/gCXZGS2qq1MZBcidYzeTGk5qOznMlCayZQKfnSNO8Zm23UK0FXJuDjvUl8/U9PZ4/e+tzoqfm1gal5+q8OK49L56Z47VzHz1fXmc01TNH3Le6Xzwzx9JWPuu8uK49L56Z47Vznz9fGsprnXeO51y3Pu9oOMIcaSmfR/eL79L9ws0cL3HT+0ca5DUjCeyWQJrm3Sp+Z347C7gs65c/Gc8JTzcop3Ynt+pDvLq1EH6CpT6Fp/wET7AzWlJTpTYOkjvBaiY3ntR0dJ4rSWDNBDo9R940r1nbLVR3FnAF4d5E3Pzlo3N0anFyd7ydYtxaCD/Bnnrofk/5CZ5gpZfiux5nuKkWgidY4rGwhJ9gX0WOaZqrijnulECn50jTvNOKWMxrZwGXpee26RA9dIMi3MqH4AmWcgtPvLq1EH6CpT5nciR6CHZGS2qq1MZBcidYzeTGk5qOznMlCayZQKfnSNO8Zm23UN1ZwBWEexNx8tMNyqnFya1aEa9uLYSfYKlP4Sk/wRPsjJbUVKmNg+ROsJrJjSc1HZ3nShJYM4FOz5Gmec3abqG6s4ArCPcm4uSnG5RTi5NbtSJe3VoIP8FSn8JTfoIn2BktqalSGwfJnWA1kxtPajo6z5UksGYCnZ4jTfOatd1CdWcBVxDuTcTJTzcopxYnt2pFvLq1EH6CpT6Fp/wET7AzWlJTpTYOkjvBaiY3ntR0dJ4rSWDNBDo9R5rmNWu7herOAq4g3JuIk59uUE4tTm7Vinh1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbjyp6eg8V5LAmgl0eo40zWvWdgvVnQVcQbg3ESc/3aCcWpzcqhXx6tZC+AmW+hSe8hM8wc5oSU2V2jhI7gSrmdx4UtPRea4kgTUT6PQcaZrXrO0WqjsLuIJwbyJu/vLROTq1OLk73k4xbi2En2BPPXS/p/wET7DSS/FdjzPcVAvBEyzxWFjCT7CvIsc0zVXFHHdKoNNzpGneaUUs5rWzgMvSc9t0iB66QRFu5UPwBEu5hSde3VoIP8FSnzM5Ej0EO6MlNVVq4yC5E6xmcuNJTUfnuZIE1kyg03OkaV6ztluo1gKuzUHH+pL5+p4ez5+99TnRU3Nrg9JzdV4c154Xz8zx2rmPni+vM5rqmSPuW90vnpljaSufdV5c154Xz8zx2rnPny8N5bXOO8dzrlufdzQcYY60lM+j+8V36X7hZo6XuOn9Iw3ympEEdksgTfNuFb8zv50FXJb1y5+M54SnG5RTu5Nb9SFe3VoIP8FSn8JTfoIn2BktqalSGwfJnWA1kxtPajo6v/7KBx/8+kG//19//bWHL7/88sXXW2/98MU1nWckAUcCnZ4jb5odyYfzJgl0FvBNJvqOSb7rDepV2t/F6y4+tXZ28bqLz1f5++Cpub7++uuHN9/8wcO77/784Sc/+fGDzjOSgDOBTs+RptlZgXBflUBnAdcE7jcvTn66GTu1OLlVK+LVrYXwEyz1KTzlJ3iCndGSmiq1cZDcCVYzufGkpqPz2115771fvnzbfDvWMCWBxxPo9Bxpmh/PLlefQQKdBVwy3ZuIk59uUE4tTm7Vinh1ayH8BEt9Ck/5CZ5gZ7SkpkptHCR3gtVMbjyp6ej8dlc+/fRPLz6SkbfMt8s0TMcJdHqONM3H+eXOd5xAZwGXRPcm4uSnG5RTi5NbtSJe3VoIP8FSn8JTfoIn2BktqalSGwfJnWA1kxtPajo6v90VfSxDn2v++OM/3I40TEngIIFOz5Gm+SC8XP7uE+gs4O9eZRQkgSSQBJLArRPQRzPULP/sZ3//oO/1HwB+9NHvbj1N+JLAywQ6PUea5pdx5ZvnlkBnAZdm95sXJz99q+PU4uRWrYhXtxbCT7DUp/CUn+AJdkZLaqrUxkFyJ1jN5MaTmo7Or7tSf3OGjhpqlLUX6K1zRhJwJtDpOdI0OysQ7qsS6CzgmsC9iTj56Qbl1OLkVq2IV7cWwk+w1KfwlJ/gCXZGS2qq1MZBcidYzeTGk5qOzr+bK++//6uHr776y3czeWa9iwQ6PUea5rso9X2a6Czgcu7eRJz8dINyanFyq1bEq1sL4SdY6lN4yk/wBDujJTVVauMguROsZnLjSU1H59/NlXfe+enDa69970HNc0YSmEmg03OkaZ5JNs+8kgQ6C7iEuDcRJz/doJxanNyqFfHq1kL4CZb6FJ7yEzzBzmhJTZXaOEjuBKuZ3HhS09H5d3fls88+e3jjje8//N3f/YeHL7744rsTkpmXTKDTc6RpXrK0e4juLOBKwr2JOPnpBuXU4uRWrYhXtxbCT7DUp/CUn+AJdkZLaqrUxkFyJ1jN5MaTmo7Ov9sr33zzzcMvfvGPLz4HraPOM5JAJ4FOz5GmuZNkMK88Af3S1gLOVzLIGsgayBrIGphdA/rYRkYS6CSgNXZppGm+lFDuJ4EkkASSQBJIAssk8Mknf3zx+ea33/5RPqaxTNW+e6Fpmr/7GkRBEkgCSSAJJIEk8AoS0N+eUf9B4Icf/vYVzJgp7imBNM33VM14SQJJIAkkgSSQBB5NQE2y/vYMNc35q+cejSgXLySQpvlCQLmdBJJAEkgCSSAJrJ+A/sYMfSwjIwnMJpCmeTa5PGdLQP8kqhbmm2/+4MU/kWqbaBHi+tevlIm+6l/BWkT+oUz9k7f6p2/l6euvvx5wuq9/4Uv3ddT5qqP+qd+33vrhoQWt96qxvl9xVD2fqtk9/HxrvdbalFd5emyU16rr55//+THYs74mzVq38vD66689+s9Ua33X+j3K4lmbjLgk0ExAPweXRv5DwEsJ5f7NEnj33Z+//KdQP/30Ty9+Sa/cLN0imKcarVvwf1cctcnql9BjTbN8qwnT0B8UVs1B67eapiMP8rf6H4ZOPajRUn3P/d7Lz7d8qFHUqH/CWddOhzJYvYHUz+WpL32vtXz6O1nfq5muPPSHidNnTjPJ90lg9QTSNK9ewTvSr01GC1LNcg1tOqtvPOVl5njaiMw8/9yfkT/V/Lxp1nVtxKdDTZiurzq0js+byPJydL3ur3CsP+CU1qpt/Tzfy8+3msTzdajanq9XXZPnexr1B8BTX/KpRrlG1fkUU/dyTAKrJ5CmefUK3pH+xxqlx67dkeWLVk7fxurtzflmfZHgmQPk57GmWZvw6UYsG+eb8zO3NsiT/sea48pAOei+ms/TN3kD0SIXqnmqpvmxn+XHri1i71syz32Ud9VUzbRqWm9iv/XgYieq5fnPpfzJ/+l47Nrp/XyfBFZNIE3zqpW7Q91qCtUkng5tNFqk99BEnPoi38u7Nl1tVsrint7gaLOVp/M3zVoH5/8XrzI4Xx8kx+8ae9Q0ly5lIY9qOIRdfehjC6f1uuefb3l7rGb6/aWa6g9Dp1msWNuq5+nvYn2vn1/dOx3ye/7ze3o/3yeBVRPQer808pnmSwnl/k0SeKypqKb5nhrF2bDUWN7bG5yjplk+1WycjmooT6+t9P1j6/sx/av7LE/ye9pMPeb/Xn6+1RCfNpOVQR3LZ711r+urHLUm1Szo69RrvVGXv9Ohpln1zkgC95ZAmuZ7q+jCfvRmQr9sT4c2XS3SpzakU/y9f6+3zefN5Mqej5pmbcznPh97U7mS98eaxsf0q7HSmj9/+/4Y9rlek4fzpulef761hvV1aegPgufN5aVnntv9+gNdvUWuN83nvvTzW5jn5iF6ksA1CaRpvia9PHvTBLTxaGM5HY9dO72/2/fatM6byZUzUH0faxD1h4Pzz04+dm0l792mWc3yY5ms4lX6zxtmaX/sZ/mxa6v4lE794aD786gXAufN5UpeS+v5W+TH/t+vx67V8zkmgZUTSNO8cvXuTHv9X32n/xemGqXHNuA7s962ozxO82k/+EyBR03zY83U6htxt2lWfc//wPBMyzfIOmqYBby3n2/56TbM8n/+QmAIb5ELWsf6+ayh89P1qvWrxkL5ZCSBe0sgTfO9VXRxP6e/gPVWRhvNrh/N0KZz+plQbdD39n95VtP8WI31f/HW5izv5x/dWW2pq7GQp/Mhj/VRDNVcPh/L4/y553iu9VleSl/VUOf38vOt+pz/LOpa/bzqWE2j8lDt617lsuJRv5O1hk9rLJ9qJOoP8/J6ns2KXqM5CTyWQJrmx1LJte80Af3S1cLUL+d7+L8zZ8OUd+VQWZw2H7Ocz+k5NVDlT8fzWqsJUQOpe1oTqzaSylx/+Dv1etp01HrXfWWyok/5qVqd+tT3581i+V3151tN4nk9y3PVTn/Iq2vye762n9PP4VNa6q1xeXnsD0V6Xv4qE63hjCRwrwnoZ+HSyN+ecSmh3E8CSSAJJIEkkASSQBK46wTSNN91eWMuCSSBJJAEkkASSAJJ4BYJpGm+RYrhSAJJIAkkgSSQBJJAErjrBNI033V5Yy4JJIEkkASSQBJIAkngFgmkab5FiuFIAkkgCSSBJJAEkkASuOsE0jTfdXljLgkkgSSQBJJAEkgCSeAWCaRpvkWK4UgCSSAJJIEkkASSQBK46wTSNN91eWMuCSSBJJAEkkASSAJJ4BYJpGm+RYrhSAJJIAkkgSSQBJJAErjrBNI033V5Yy4JJIEkkASSQBJIAkngFgmkab5FiuFIAkkgCSSBJJAEkkASuOsE0jTfdXljLgkkgSSQBJJAEkgCSeAWCaRpvkWK4UgCSSAJJIEkkASSQBK46wTSNN91eWMuCSSBJJAEkkASSAJJ4BYJpGm+RYrhSAJJIAkkgSSQBJJAErjrBK5umkWQr2SQNZA1kDWQNZA1kDWQNZA1cO9r4NKfCv7mEiD3k0ASSAJJIAkkgSSQBJLA7gmkad59BcR/EkgCSSAJJIEkkASSwMUE0jRfjCiAJJAEkkASSAJJIAkkgd0TSNO8+wqI/ySQBJJAEkgCSSAJJIGLCaRpvhhRAEkgCSSBJJAEkkASSAK7J/D/A7elKxwIeFEAAAAAAElFTkSuQmCC"></p>
<p>The relationship between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> can be modelled by the regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> with&nbsp;equation&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>, where&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mo>&nbsp;</mo><mi>b</mi><mo>∈</mo><mi mathvariant="normal">ℝ</mi></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use this model to predict the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>18</mn></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>x</mi><mo>¯</mo></mover></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>y</mi><mo>¯</mo></mover></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the line of best fit on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>At a caf&eacute;, the waiting time between ordering and receiving a cup of coffee is dependent upon&nbsp;the number of customers who have already ordered their coffee and are waiting to receive it.</p>
<p>Sarah, a regular customer, visited the caf&eacute; on five consecutive days. The following table&nbsp;shows the number of customers, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>, ahead of Sarah who have already ordered and are&nbsp;waiting to receive their coffee and Sarah&rsquo;s waiting time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> minutes.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The relationship between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> can be modelled by the regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> with&nbsp;equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of Pearson’s product-moment correlation coefficient, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret, in context, the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> found in part (a)(i).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On another day, Sarah visits the café to order a coffee. Seven customers have already&nbsp;ordered their coffee and are waiting to receive it.</p>
<p>Use the result from part (a)(i) to estimate Sarah’s waiting time to receive her coffee.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The number of hours spent exercising each week by a group of students is shown in the&nbsp;following table.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The median is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn></math> hours.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the standard deviation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Sila High School has 110 students. They each take exactly one language class from a choice of English, Spanish or Chinese. The following table shows the number of female and male students in the three different language classes.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
  <mrow>
    <msup>
      <mi>χ<!-- χ --></mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>&nbsp;test was carried out at the 5 % significance level to analyse the relationship between gender and student choice of language class.</p>
</div>

<div class="specification">
<p>Use your graphic display calculator to write down</p>
</div>

<div class="specification">
<p>The critical value at the 5 % significance level for this test is 5.99.</p>
</div>

<div class="specification">
<p>One student is chosen at random from this school.</p>
</div>

<div class="specification">
<p>Another student is chosen at random from this school.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null hypothesis, H<sub>0&nbsp;</sub>, for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the expected frequency of female students who chose to take the Chinese class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
  <mrow>
    <msup>
      <mi>χ</mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether or not H<sub>0</sub> should be rejected. Justify your statement.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the student does not take the Spanish class.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that neither of the two students take the Spanish class.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least one of the two students is female.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.iii.</div>
</div>
<br><hr><br><div class="specification">
<p>The manager of a folder factory recorded the number of folders produced by the factory (in thousands) and the production costs (in thousand Euros), for six consecutive months.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-16_om_17.30.09.png" alt="M17/5/MATSD/SP2/ENG/TZ2/03"></p>
</div>

<div class="specification">
<p>Every month the factory sells all the folders produced. Each folder is sold for 2.99 Euros.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a scatter diagram for this data. Use a scale of 2 cm for 5000 folders on the horizontal axis and 2 cm for 10 000 Euros on the vertical axis.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data&nbsp;the mean number of folders produced, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
  <mrow>
    <mover>
      <mi>x</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
</math></span>;</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean production cost, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar C">
  <mrow>
    <mover>
      <mi>C</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Label the point <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{M}}(\bar x,{\text{ }}\bar C)">
  <mrow>
    <mtext>M</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mrow>
    <mover>
      <mi>x</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
  <mo>,</mo>
  <mrow>
    <mtext>&nbsp;</mtext>
  </mrow>
  <mrow>
    <mover>
      <mi>C</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
  <mo stretchy="false">)</mo>
</math></span> on the scatter diagram.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the Pearson’s product–moment correlation coefficient, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a reason why the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
  <mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> is appropriate to model the relationship between these variables.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
  <mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
  <mi>C</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the equation of the regression line to estimate the least number of folders that the factory needs to sell in a month to exceed its production cost for that month.</p>
<div class="marks">[4]</div>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p>A biased four-sided die is rolled. The following table gives the probability of each score.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of<em> k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected value of the score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The die is rolled 80 times. On how many rolls would you expect to obtain a three?</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the hand lengths and the heights of five athletes on a sports team.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The relationship between <em>x</em> and <em>y</em> can be modelled by the regression line with equation <em>y</em> = <em>ax</em> + <em>b</em>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</em> and of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Another athlete on this sports team has a hand length of 21.5 cm. Use the regression equation to estimate the height of this athlete.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A survey was conducted on a group of people. The first question asked how many pets they each own. The results are summarized in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The second question asked each member of the group to state their age and preferred pet. The data obtained is organized in the following table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
  <mrow>
    <msup>
      <mi>χ<!-- χ --></mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span> test is carried out at the 10 % significance level.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the total number of people, from this group, who are <strong>pet owners</strong>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the modal number of pets.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down&nbsp;the median number of pets.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down the lower quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, write down the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the ratio of teenagers to non-teenagers in its simplest form.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State&nbsp;the null hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the alternative hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom for this test.</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected number of teenagers that prefer cats.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>-value for this test.</p>
<div class="marks">[2]</div>
<div class="question_part_label">h.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the conclusion for this test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">i.</div>
</div>
<br><hr><br><div class="specification">
<p>A transportation company owns 30 buses. The distance that each bus has travelled since being purchased by the company is recorded. The cumulative frequency curve for these data is shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>It is known that 8 buses travelled more than <em>m</em> kilometres.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of buses that travelled a distance between 15000 and 20000 kilometres.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the cumulative frequency curve to find the median distance.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the cumulative frequency curve to find the lower quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the cumulative frequency curve to find the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence write down the interquartile range.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the percentage of buses that travelled a distance greater than the upper quartile.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of buses that travelled a distance less than or equal to 12 000 km.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>m</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The smallest distance travelled by one of the buses was 2500 km.<br>The longest distance travelled by one of the buses was 23 000 km.</p>
<p><strong>On graph paper</strong>, draw a box-and-whisker diagram for these data. Use a scale of 2 cm to represent 5000 km.</p>
<div class="marks">[4]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>The random variable <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> follows a normal distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#956;</mi></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#963;</mi></math>.</p>
</div>

<div class="specification">
<p>The avocados grown on a farm have weights, in grams, that are normally distributed with&nbsp;mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#956;</mi></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#963;</mi></math>. Avocados are categorized as small, medium, large or&nbsp;premium, according to their weight. The following table shows the probability an avocado&nbsp;grown on the farm is classified as small, medium, large or premium.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="data:image/png;base64,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"></p>
<p>The maximum weight of a small avocado is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>106</mn><mo>.</mo><mn>2</mn></math> grams.</p>
<p>The minimum weight of a premium avocado is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>182</mn><mo>.</mo><mn>6</mn></math> grams.</p>
</div>

<div class="specification">
<p>A supermarket purchases all the avocados from the farm that weigh more than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>106</mn><mo>.</mo><mn>2</mn></math> grams.</p>
</div>

<div class="specification">
<p>Find the probability that an avocado chosen at random from this purchase is categorized as</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mfenced><mrow><mi>μ</mi><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>σ</mi><mo>&lt;</mo><mi>X</mi><mo>&lt;</mo><mi>μ</mi><mo>+</mo><mn>1</mn><mo>.</mo><mn>5</mn><mi>σ</mi></mrow></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math> and of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>medium.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>large.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>premium.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The selling prices of the different categories of avocado at this supermarket are shown in the following table:</p>
<p><img style="float:left;" src="data:image/png;base64,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"></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p>The supermarket pays the farm <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mo> </mo><mn>200</mn></math> for the avocados and assumes it will then sell them in exactly the same proportion as purchased from the farm.</p>
<p>According to this model, find the minimum number of avocados that must be sold so that the net profit for the supermarket is at least <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mo> </mo><mn>438</mn></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Fiona walks from her house to a bus stop where she gets a bus to school. Her time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> minutes,&nbsp;to walk to the bus stop is normally distributed with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>12</mn><mo>,</mo><mo>&nbsp;</mo><msup><mn>3</mn><mn>2</mn></msup></mrow></mfenced></math>.</p>
<p>Fiona always leaves her house at 07:15. The first bus that she can get departs at 07:30.</p>
</div>

<div class="specification">
<p>The length of time, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> minutes, of the bus journey to Fiona’s school is normally distributed&nbsp;with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>~</mo><mtext>N</mtext><mfenced><mrow><mn>50</mn><mo>,</mo><mo>&nbsp;</mo><msup><mi>σ</mi><mn>2</mn></msup></mrow></mfenced></math>. The probability that the bus journey takes less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math> minutes is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>941</mn></math>.</p>
</div>

<div class="specification">
<p>If Fiona misses the first bus, there is a second bus which departs at 07:45. She must arrive&nbsp;at school by 08:30&nbsp;to be on time. Fiona will not arrive on time if she misses both buses.&nbsp;The variables <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> are independent.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that it will take Fiona between <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> minutes and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math> minutes to walk to the bus stop.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the bus journey takes less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math> minutes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that Fiona will arrive on time.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>This year, Fiona will go to school on <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>183</mn></math> days.</p>
<p>Calculate the number of days Fiona is expected to arrive on time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f(x) =&nbsp; - 0.5{x^4} + 3{x^2} + 2x">
  <mi>f</mi>
  <mo stretchy="false">(</mo>
  <mi>x</mi>
  <mo stretchy="false">)</mo>
  <mo>=</mo>
  <mo>−<!-- − --></mo>
  <mn>0.5</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>4</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>3</mn>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mo>+</mo>
  <mn>2</mn>
  <mi>x</mi>
</math></span>. The following diagram shows part of the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f">
  <mi>f</mi>
</math></span>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-15_om_06.09.00.png" alt="M17/5/MATME/SP2/ENG/TZ2/08"></p>
<p>&nbsp;</p>
<p>There are <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>-intercepts at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0">
  <mi>x</mi>
  <mo>=</mo>
  <mn>0</mn>
</math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = p">
  <mi>x</mi>
  <mo>=</mo>
  <mi>p</mi>
</math></span>. There is a maximum at A where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a">
  <mi>x</mi>
  <mo>=</mo>
  <mi>a</mi>
</math></span>, and a point of inflexion at B where <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b">
  <mi>x</mi>
  <mo>=</mo>
  <mi>b</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the coordinates of A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the coordinates of B.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the the rate of change of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> at B.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> be the region enclosed by the graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> , the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis, the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = b"> <mi>x</mi> <mo>=</mo> <mi>b</mi> </math></span> and the line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. The region <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="R"> <mi>R</mi> </math></span> is rotated 360° about the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x"> <mi>x</mi> </math></span>-axis. Find the volume of the solid formed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 7 adult men wanted to see if there was a relationship between their Body Mass Index (BMI) and their waist size. Their waist sizes, in centimetres, were recorded and their BMI calculated. The following table shows the results.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAigAAABKCAYAAACRrq/9AAAgAElEQVR4Ae19D3hU1bXvLwO11gLlUrhyAj7zSCDgBfWRCFbpcwgykVIRQdCLJoF4LVSo1DyYNFzw6dViYfJCbeFelSYSuFJBZxqLXM3EGagX6k06oXDhK0waclGTGVq8lPypyJ+Z/b595pwzZ86cSSb/JjOTle+Ds8/+u9ZvrbPOOnuvvSeFMcZAf4QAIUAIEAKEACFACMQRAoY4ooVIIQQIAUKAECAECAFCQERgqBqHlJQU9S2lCQFCgBAgBAgBQoAQiCkC8sJOiIPCKZALYkoNDRZTBLgjOpjkPNj45cpEPMf0kRqQwUjGAwJ7TAcdrDKWQaYlHhkJuhIChAAhQAgQAoRA3CBADkrciIIIIQQIAUKAECAECAEZAXJQZCToSggQAoQAIUAIEAJxgwA5KHEjCiKEECAECAFCgBAgBGQEyEGRkaArIUAIEAKEACFACMQNAuSgxI0oiBBCgBAgBAgBQoAQkBEgB0VGgq6EACFACBAChAAhEDcIkIMSN6IgQggBQoAQIAQIAUJARoAcFBkJuhIChAAhQAgQAoRA3CBADkrciIIIIQQIAUKAECAECAEZgZ47KG1OFKemICUlG8XOz+X+AHwOZ3G2eNR2SspslNZ3BMv8Z1CRm4qUlFTkVpyBP1gSIXUdXtuqQF8FNngj1NLPbkODcx9KV+1A/XX9GmG5fi/qK59Dse2zsKKBz/gMtuLnUFnvjQK3gadWoUDRE64r/N9SVDR8qRQDbWio2YYCUZdSkJJagNKaBqi0RlU3gZJcl97di9KCaeHPiN+Lum0FSBXxyEWx7UyC8utHm3ODxIcsX/mqlbPaLvA60dqAOJR5RwNqSmX5pSC1YBtqGtpUhPrR0VAtyZ7zmoviyjp4uzZ4qj7iK+n31qGyODfwDEd4Rv3eo9gm6nsKUmZvgC0Ek/jip2tqrsJbvwfFs/n7Sk/GvIdEsl38ffgu3iktQEaxE2ptDWKh5nkaCrYd1dfZLm16sMfepnruoAxLReY0AYAHx899Hnxp+j/HueMeiS43ak40B8s6PHCf5G7GLDw6Kw09H7xrtq/Xv47vzHkM6z+83HVlXqPjFCpWPIh17m/jhwtvia5NTGvdgoU//Dbc6x7EiopTCfJCu4qWD23Yo/YsTQ9gVsaNEnJX0WLbAGPBKdznbBV/H8hX/wQubl6BF0Oc3pgC3evBREO9woQHbR6kFVjRzlzYkjNa6vcSfl91FHhsJzzsCjy1C3B+zRMJyu9FuKrt+h8OIXIG/C0f4c099Sps+98GqAbru6T/E9jWLkbByRw4231g7ArqC9qw2fgTONsCHoi/5QPsPAgs2HFCLBdlXLIQy8rqEuS51cDVUYey5a/h4uJd8DEf2p05OFmwGGttn6hs+wlU2YfgsTdOgvk8qF3QgjUqTDQ9xvmtHx31O7D8Z21YvPccGGuF875TKDBugK3lqkR7ItmuL9FQ8SxeqNyFZ9bvxhe66Ad4XrauCbmcZ98HKLjwso7OdmXTdTvveSZT/QV+K1CV0WmynbksRsbbIN/KPFJdn7ucmXie/E9Vds1lYek8XyhhjlZfp733tlAZK93CXNe66M13jlkLpzKh0Mqa+5esLgjputjXbGWFwlRWaD3Hekpq9+TcNU0Ra7TXMotpU2RZ+06zcpPABLODtSqdXGbu8iWaPKWwR4mY8cup4zwbs1h+2RHm0RGQr/EIO9R8RcXHBeYwZ/Upv7zzmPDceohZNtk1fPpYq2MTm19+WqWff2EuSz4zOy6o+O77ZCx4Dti3rFBeRD2+R8q7zBoPfayxIwGd7mu7Fwt+GdN7Hq+wZutqJih2XIfnVgczCxqc+kDkMeE5RJ4S0fI7QrZViWi7dGmW+eO2WNZhKU+U4RJW7r4clFxXNj1Ys8cptYx7MYlxEyZO/xb4HAqONsEjLqN8icYjH8AOASZzEZbxshoXTotfFl+i6UQdzvK8udmYMoIPrZkiE6fSSmFTljH0lnj49KkTFfJ0ozxNXuFEQwf/ggm0+Ur2+sBYZ9cj+yspyCith/5Kz1W0VFmwpuJWFD2dg3G9QKTnbmL0LQ3j/jcez/sqKtZYUKV489G3j11NP9rqqlBm/wVe/HE5bE6dZRvDaKTdmQpv3Qn8UZQdp64Dze4vkJd7O0bEjtg+GukS6l/9J5RN2IDNa++FoKNLhvR7YRx3Q3A8ccbxFhQtnZ5w/Pr/egseNs8J5dPfgHe2nMUi9Qxp2zHsL9uNrS9aUGE7LD2nQQgSKWUYm4Y7BQ/qjjUFZ0P4zPDZ+5CbPQrAjUg33q2xIzdgbFpGwFYmErOcVv85HNl3DNMyUzFMof0GCFOnY5rXjmrXRV2e/efP4Xjm41g6g2OSWH/+xt9in30cMscHOYbhZky9dwq8ez6Ei7/Pksx26fI84nbk5rVg35Fz0kxZFDa9r0WtdnPUnos6P2LaY2X54kyJ5GVJHhqwhJWfPiZ+HQOyFx34UgQEZhK/riQvXJ5pUV+F1cwqfmVeYx7rytBZGvELVQjO0CjtBGa01LJ2pmqjlIGlW1xMdyJF7k/5GpC5vcI8roPMWm5mJmVm5QrzOJ5nRoUHua766mPt7g+YJX+qRKOJmXfVSl+ZqlknTlv+68xhL2P5Ap9xEpixxM4815qZo8QktZ3K8stPsnZ194x/oZYwoVMaQhqE3XRbzmE9RJGh6II8myYwo9nK3O3qaQUfa3eVMSPAhPxd7HT7ZeZxWJg5wuxDFKPqVokJv4yxwNe1iZnLdyvyF/LLmN0dnB8KEsj1xMHKzStZiaNZNdsQrNGbVKx41tLIMZivPC+8VJo9UD2LMJYwqy4m2t66dx8bnvls0HwGSM+mr5k5NpWwslpPJzIMPLPpIbh0jze92jHhV/yKlm22iopI+ayVuR3lzJz/EnN41DOFqra9SPY/z7J91cwcKHZXzk9A2xVxBiXSDJ/0zjaVMzc321HZ9F4IV2qqljFf91f+1AVKZmcJhWDJCRGVFgzisopsmCTlvuZilnT+sjIyi6tdxex8ZnH9RRwlsHyhqqN2NqSlImXpRnEogooiOkbSdJRSr4slHqWeaimKqccVDSun8b+Vl2nQydKC42Ptp3cFHA5RqFqnTCNkoZCVn25lQb7TmdGYxYT8cvax1cwEcWz5gQiOpSyjyYoTLIoq1W05R9VrhEo+D3NVvc7MRu5Uyk6kuu4V5qndrjhpAedVXd77dGz4lfTdaGa7XNLLqv0kK+eOqrGMuUIcM1kvJMc0zHFLFJ61dHIMVoYufyhVuMN/gJWbJec7DBOlYo8TsZEzf4Y9rLYsP+LzGc4Al3e+YufCy3uWExN+ZRuvtTWirZc/PiX6Zfsv2i0TM1tPaz6uesanulUseA7YV61TJjkuynuHU5Vgtiuig6JxRBTAI+R3adOVDnqUUMtYZxK6G3M00jQXUA/rsSZcdH0oBkQKi6dj4tAbMeGOGUiHF/Z9v0VD4wnU8PUd4VuYPvEmwDAZhdUeMN9OzG52wmbbiZIn1qBCDKhsx4VW9U6PIE2GsRNwH19X8r6MOZNXoPSdKtg/yUSp5woY24/CSXIAZrBN5NR1XPikMbAUFFJpKIRFr4K118Ji5IMdRFnZc9h+dAb2+hgY86C6cLJOkO9F1L3xc+z2CjA9eg8yDKMwY+njMOKbGD/ya4ERDF/HyLE3BdJz52Pe5BEw3HwrpohZZ+H+Hz+Ac8dy3P2tmZgr1rqAi+2hi1OG4SMxlpfZ63DqT6FlgY7j6H+DgKyHnsIWx+/gKJmGw2VVqJOCCQNUDsXwkeMxrehlmI2A/cm12OhsCQbfxRErnZPCl6aaIMzIxcNZQkA3hk3F8n98FqbDFmzY36DiaTRytrjEYELXrjxg62IY11ahJYF3eYjY8OUA299KSx1atG6AkPVdFG45AI/jeRgPv4n9dXx5IAH/+DN8axaKLEUw4m08uXILnF45eFLLDw8+3IvKMauxKmuktjD+7w2T8Ejxcgj2bfjxLik4n+9Q+1U16rwTQpdBRuRgi4fB56nFLjNX6yWhgbTxz61IoWHSAhSbU2HfaMGuM4H9Ln6vC7+qrod3WgbGD5Nfm8liu7opmC5tejf766S6jHQnVTorGokpM7PFCmdr3kPFQR7Rn6XEDwydOB2L+fv9pBunTrlxktdUxZ+cqXgSqUNSkb1wMRYv/h62Hpa3ewzHmG/oOxqGcd/FSwd2w8wdB+9urF/C285HdmoaZhfburm+/SU8TW6RfmHsSHxdy+qwbHxv03Jx7dhbm4a5T+vHFSjNrn+CY1a+U+EmjB35dRhgwLCsZ3GInUT5olt1HBqlpZRIx9yHcjBZeQC05dp7N5o8+o6ctuaA3xvGIedHxTBDXrfmFPnRcWYP1pb58PdFP5KcGODlOStRVn9pwEnuFgEhu9eCLQ0Z9+BRE38EPMGYBbmYP+gFL+C18iXwvu+CW4nDkSsk1pWvY9v+zohsMb4sEu03QMhZjU1mYE/1f0bY7hipbTzkt+FMxXMow0MoWvf/4PDYUYLXMGfZDtTrya/DhZ37/wYlq7JVMRzxwEe0NBgwIudHOGwvBDZOw/CUaSgo+xAn/nAchzU7teQeDcIMFLz8CspN/433a8+G671cMW6vo5GzaS/sRdexcco3xKMPyo6ewB/qzkofnpzwJLJdGIbxmROAk41o1tPhSHLStemRKvcsv5cOylDcPHUGTHxs+4tYX1YPCKbgF5QYZJMFeLdiyZKt8PLg2ftuw81cvA3vYO2TFfDCBHP526hyeeC75oIlvStG+JdYHrYc8oC1u+GwWmF924J8wYvDW9fgByFfql311VW5ASOy70ced7LO1uFEUxfOwBetuCDu4TqLo01/jhCU29WYSVwubk3PDH51+Ruwf+2LaJ5xWyDQkiv85n1wWYD1G2xoSKQZBTlo7vg5nA+j+yZNkKFaxjciY9YDgWdInZ1waR4gX4e/iyq4mRvEzE4wiV/mA3bLgxlTbxY/OAzCXGw+UAULdmhmybiR+wTv7vwvzNv0eDc+OuKR9xGYNPdZVHr47PFJVBbdBRzvgLl4ASZFeoMY0jDr0VnxyEx0NA2bhLnrKuFhDMxTiaLbh+C4eymKH5kU+NBMJtuFCDZI/Oi6pHLKdKDT2nSdKr3JiqReUfcZiGoPVhfy7ld9QUmemVKcijvTRsPAvc/mxsCMijARM3MX4KGsb+JPH72Hg+I2H6WBJsH3nq8JHAw1+wU429OQs2gRFi1agofmTdXUjeb2RqROyBQres9fwl+1TTrOwPb6MYzJ4y7YEVU0s7aidK+cDQOcPfgRTnTHG43QZefZmZiQqj/T1Hm7ASrt8KAx60k8Ii/DiefiaHflj8DE6bcn4I6HUcjONUE4eQyn1NP9Io/TOzn3J/AsnJ2XjcyoZ84GSH6dDdvp8o62YQeaG6cFjb22OG7vVXZLTeOwCZg+g392qf78LXC+8j6GP/Zw0DnpOIXKiqMJOGuk4WvjOuyZuw2blLN9VOVKki95tmLezPQEnTlSGIHfW4ONKw9g7gEzcuTZwaSyXYA40zvtN9KuLIn3Lm0X33SpselB2PompY5iUQenqPM7T4cG/GmDHJWATh44pQowCgaGyrs8+DWLGY3p4jVwZoJqR44cxCrvuhEDsdRtef/y7h95R0WwPNIuHoU+vf6l/pQ6Iv2Xmcf1sWY3ioyQOmB3avAsjHY3czjcgYAxOeiM0y+PqQSXBQOzlDGVXVDyGCretIFrwSqdpnom5067DCv0eVysqsqlnJHh8xxhZWaLJrJf2hEhBQuLnYiBpcZenfOiJSYW/IpjymcliDuSfFIwZSEzibvLeA1p55oqkNbnsbMS00oxWFpLd2/uY8azRCTX1/nyGRFqwsWAuoPMJe/oEANMS9imRN25JNmfwK4zcWtDIDA+PWh7WPtpZpWDgUPsVPD5VkPU03RsZcx357zFLPnGoF2TCRf1PosZzbslOQd2O5rk50Cu1wfXmPLM7fbbFpafnq+zSysBbVfEIFkuGOndZXw+YKP57rSS+dLO2IDgorPpvReyWsa928Uj0iLv1uHOQPiOE6bs3gFDyAuVR/XvlnZ3gEE02p+yZmlbceDwLh0HhY/JFafcLG5P5cyIu0PM5cyh3roYEmmvt3tEAlJ2GGTnSXYWQrZCtrLT5YXi1t7gQxhJEBq+hHxmscovas02Y/Dtz2+xt/K5UyY7U0ZmsZZL27flvJXM6pE3Scvb4Hpu7NQKEImL3uaLL15x5w53HPOZ5e1D+k4df4HtUsmS17VLzlxviZDax4JfhdR2N7Nb5B0e6i3mvIZql5co76ks32INvryVTnqfiCnP4lZis/4uFdHQqbbNW94KfU57z6rSQ6x49nlq2S6VAxKylVxyUjkt4f907KNCffcTseFX/gDlxwRobKxCsmwfJZ5DbJ5SqU8SMeFZfgeAHxng0LdbnJuEsV3yO0Otk3q6qN6VpLVdnF07K4nGpvdS0moZp/C+5LkY/psDqls5O8mvfNmoCHct/g/kOT5QHUker2zz3zR5AHP23A3r78qwSH3oV5QkDzY5DzZ+uRoQz1E+DAlcjWScwMKLkvTBLuNex6BEiXMcV7sB4xaux/bCK9jz5kdxv9Uz8JsmV1C4fT0W9sA5iWNBEGmEACFACBAChICCADkoHArDrVj0yi/x0vWfY8MrEX7BUYFs4BJisNYTm3H9pV/ilai2LQ8crTQyIUAIEAKEACHQGwRoiUeNHj+AaM+/YP/wp7BlUbz9ovFnsBXvRPvS7yNPPghMTXs30oNt2nCw8ctVgXjuxgORoFVJxgkquG6QPdhlTA5KN5QlWaoONqUfbPxyPSWek+VpjcwHyTgyNslSMthlTEs8yaLJxAchQAgQAoQAIZBECJCDkkTCJFYIAUKAECAECIFkQYAclGSRJPFBCBAChAAhQAgkEQLkoCSRMIkVQoAQIAQIAUIgWRAgByVZJEl8EAKEACFACBACSYRA2C6eJOKNWCEECAFCgBAgBAiBBENAPtF+qJZuuUCbT/fJg8Bg27o22Pjlmko8J8/zGokTknEkZJInf7DKWJYgLfHISNCVECAECAFCgBAgBOIGAXJQ4kYURAghQAgQAoQAIUAIyAiQgyIjQVdCgBAgBAgBQoAQiBsEyEGJG1EQIYQAIUAIEAKEACEgI0AOiowEXQkBQoAQIAQIAUIgbhAgByVuREGEEAKEACFACBAChICMADkoMhJ0JQQIAUKAECAECIG4QYAclLgRBRFCCBAChAAhQAgQAjIC5KDISNCVECAECAFCgBAgBOIGAXJQ4kYURAghQAgQAoQAIUAIyAj0zkG5Xo/SjBTxWG1+JG/ov1TMLt6Deu9VeSwAn8FWkBGsV2CDV1UKfA5ncXawPKMU9dd5hWC7jNJ6iFkh7cJv/N46VBa/AJs3mtoAvO+iOIze8H4phxAgBAgBQoAQIAT6H4HeOSid0ufF4a35yF62A/Udfv2aNS6cblOVXf8Ex6z1+nWjzvWj40wlVmRtgjv3H7BQCPu5If2ehHn4YW4T1mV9HxVn2vTrUG43EfCjo+EwbO+UoiBjA5xqWSs9XYW3fg+KZ6eKjmlqwTbUNCQq/m1oqNmGglTJWZ9djMp6L1QaLnGt5nkaCrYdhTe8koJQXCc6GlBTWoBU8QNF76MEQDR14ppJNXFcp6tRWjBN+pDKRXFlXbj8/F7UbZNxyUWx7Qw61N0kVDpavfajzblB0gXpGcitQEMi6na3dfYqWmxrkJqo/CJKvVb0ltuwf8M70rOfWuxEf1jtPnJQVsLquQb+Q4PyP1+zFYUCgMNvYn/dRYWtkITXjmpXsMzfdAI1Z0NqdPvG31KFtTmlGLr9dbyUMw7RM3gDhJwS/Ov2r2FjzgbYWtQzP90mgxoA8DfswmMvvAHrM+ux+ws9SPzoqN+B5T9rw+K958BYK5z3nUKBMRHxv4qWd/fgIOZjh4eB+TyoXXAeJdlPoaz+kor5AM/L1jUhl/Ps+wAFF17GsrK6xHuB+T/BuzudwIKfw8MYfJ63seD81tCPkmjqqNCJ96S/5QPsPAgs2HECjF2Bp3YBzpcs1MjvEn5fdRR4bCc8cp01T+BF5+fxzp4OfdHqNX/gP8OHbx5QzYoLMD16DzKiN8I64w9AVg901t/yHp5bs0PF+wDQ3Ysho9NraQDR+X4KWQ/uw7m0FTjc7oNnSw5G9GL8iE2Z6g/g/kU3/q65mCUdDFjJrJ5rmoafMmt+OgPSWb71U6ksmLfMvJaZACaYHaxVLL3M3OVLGJDF1ppXsnSAId3CXGK3cjuwdIuLaUdSBvadY9bCqQzGMuZq9ynZ3Uq0OphZABMKray5h110a7wBqNxtOfeKRkmuQglztGoA9Z1m5aZ7mNlxITiCJMOgXgSLepqKCb++Jnbo0KcshEORP0Gl44wxPZ5FnVvCyt2Xe8piWLtY8OxrPMIONV8JGdvnLmcmZCkyjaZOSAe9uOl/ni+zxkMfa+xCuH6H83yBOcxZoXrQCz7lpv3PL9fXKPWa+Vi7q4yZFHsuU9m311jwHC4/xrR6HcJVey2z5K9l5vypDKZy5g4xAiE1u30TC34Zi06vA8T/hbks85mQv53VekKf/W4zF6GBmud+8m35MosT7/LpEOEBPDTz5jAHaehdJjxqEuC1HsMfeZiI/xyO7DsCCCbMuz8trH7XGX50/N6Gn1ecgjDjDkwcpsNaRwOctp0ozv2hNEMiTculfBel8lfuiNuRm5cFb8VbqG78suthqUaPEfA3/hb77OOQOX5YsA/DzZh67xR493wIl+6SULBqXKUM/xNG4y2hM3aG0Ui7MzWETF2eRZ1rwb4j53SWg0Kax9WNIf1eGMfdEEKTYWwa7uQzp9JfNHXkuvF/vRHpxrsxLsS03ICxaRlQsYwwnv2f49zxW1C0dHr/fGX2J3BR6jVwEXX734R96xb8uMIGZ8Iu0yJcfgC0eh2E/BLqX90LPPM0csd+NZidUKno9Bp8Gaj+DawrS8P2zU9hhhD67PcHyyGPWs8HeA2LU78SDG5NGYLhU5ZjN/JRVvWPWKgxYuI4hjTcMTcTOFuHE01fAh0euE96gbnZuG1UlHEjIQR/AfehX+Mw0jF35kQdQ/AZbKu/gzmLv4et9vfwbu2fAmSMHINMHEPNifPSy2EYxmdOAHAk4V4YIXDE/Y0fHc2NOBlGp2TwvY04dz4Zltm+iXkz0xFwwb5E45EPYBcykDZW+3BfgX3fb9GYiOv1WhnedDdmZnYx4RtNHW2/cXx/07xsZIZ9FPF1fScqSn6KxuLtKMoaGcccdJc0tV7z5dxfY8tWHj9ox9YnF2NO5pIEj7vRwSNMZ/kLezd+hmVYlTVKp0HiZ4Xotb8B+zfsAPLugP+XTwVijVILUFrT0G/L033koEQQhHc3LDtscIXs5JHrfh0Tp38LgugINOGS60Ps8Qow3Xcbwudb5DadXf+CT05+1kmFW7Co8j/gMGcB+ALnL/0VfvC4k/+DUstSPDorTfr6HYrhI7myeWH/zR8QcGM66ZaKeoiAAcPGZ2BaJEdQ9yXew6EGqlnbf6L6+AN42iTPrHSg2d0ETMvA+LCX2UAR2Zfj+tHmOozjq/Jh0vsoEYeKpk5f0tTffV2Eq7oFq57O0cys8B2JMzA8cw6e3PprfFxdi8ZImwX6m8S+7j9MrwHDpEJUi3FILlSVm2HkjsridXhVnpnuaxpi2l8Ene1w4dWfAc+sypY+QGJKVD8PFq7XgdnfdMy47Q7cW1QJD2vF6ZeGosxU1G9y7iMHJTxIlrWfhtVsgnf3Giz86RGdCF8DRmTfjzzBC/u+t/CLg3Z4MUvlKHQT/+t/RtNRHmE7EmNHfi1C45GYMjNbdD7OXuQOCt9h4MaJUXlYOunG8DZHm+CJcpdyeGPK6QoBw6QFKDanwr7Rgl3Szim/14VfVdfDm/Av8Uuof/3XGLN5BbKS0hnRkW6HC69Xjsbmzgx2NHV0uo7PLP4FvReVY1ZjVdjsyGjkbHGJwdKuXXnA1sUwrq1CS8LPkHWu1wYhCw8VboHDY0eJ8RjK9h/Tsf3xKc2IVOnq7CXU73RiwuZVSfh86+m1NOMtZCH34WwIoucwApOXr8dLpmNYv8HWL7u1+shB0RHtsMlYsHQu0rk7IMeZaKuNmIiZc9MB+4tYX1YPmB7ArAwdR0Hbrg/uv7jQii9wCfX73bhj6f9KQg+4D0Dq9y5GI2fTXtiLrmPjlG8gJbUAZUdP4A91ZxMz+l/Biz/gb2H/qH/QvLik5cOTjWhOlq9phWdusN/HqJLlnRjsaOooHcZ/osOFnfv/BiWdOWQGAVkFL+C18iXwvu+CO6HlHkmvw0VlEObgR5uWA4kWSxbGip7OBnCw3vr3+uELYX0kWIauXl/F+XON4buUDGmY9egsoJ9sWv85KP4WfGStgbhr+N4JSNUNKxmDqfdNV6Qn3JmGsT2laOjfYsK93B26hPOXLit9hiaGYsytGQGn6fxFnK//N5y44zuRDWpEukN7pbteIDBsEuau49OFDMxTiaLbh+C4eymKH5kUGnDaiyFi3VTcsndqFjYVTtU4vjciY9YDMGkJEoMoLyWwU8a3or6FU/OeReHkSLEn0dTRAhPH9+JW1P/CvE2PY3KXM2QR5B7H7OmRFlmv9WpLS7gJPRMaSWd5QPAv8PLiNAxRDigdgzk8Bsf+JDKHpCK34kxCBbwrEoyo113EBvaTnHvqDij8BBLaINkUpAwZjzkv2wHMh+WZnJAo92Bj9YObhbzc23WCW4O1O0+FOjud1wXw6QGUn8jE0rCp2etov8TPZulNPEyXo1MFHQT83hpsXHkAcw+YkTOij1RTZ5z+zPJ7nXhl/414LE92TviOtndQcThwBoYh4x48Ou03Ief/BALEp/d8ebM/Geqy76vwOiuwf/iDyFOckzacqdyDw287S84AAAQtSURBVMourGjqdDlQ/FTwt8D5yvsY/tjDQeek4xQqK45GWM4ITI+f1Q2kjR+2OqOkK70Ob8t5/jOyihdgUkI+yp3p7KjA8p3q3C/GLgTiG03lcPs8qC6cnHgfWJ3qtRyScRpHT/1J5XzxuLqWfvu46lfVEfItsLp2dhq9LhpskyBuL87N7k0ktOzsnEVN7R8jGAr1Y3Qnluou7UiBjL2Jh1EPQ+muEeDbv98pxYpv/yvGbPnnTvWl684GqgbfsWFDybInUFQ0B6lD5J9+4Dva9gOp0lZqwyQs3fwI6l7cAScPHudG4SdlqCtapx8HNVDsRDVuGxpsz2PZnO+jaM541dfkNzBl7zWkijML0dSJarD4qNRxBraSQswp+j7mpH41uHNxuAl78U0Mg3R0geoUYb/XgZ9suYgN6+/XBNLGB0udUxGNXgdOFX1XOTX5Krx1r+PHh7PwA+PozruPy9Ik09loMO5SrwGMmIVntt+H99f8kxQzyOW8D5XHH8Hmpf00460+K0V9QIo6P2HS8kFteoeCSUxcc1lYOuYzi+sv+mzRQW36uPQkV8KS61Xgn8BM5aeDh5kp5SZmLncwd08P1+uCtljota/ZygoFmU/NNezwpivMU7ud5Yv1Tcy8q5Z5+vBwJw5H//N8hTVbVzNBka2aZ1nO0dTpQnjdKO53nmX7osuzfNCej7Wf3iXJlmMyleVbrMzVD4da9Tu//Jy2qPT6CvM4nmdGCRch38LedrhZezdkF23V/ue5pzobOIwvIQ9qi0qvZQm1Mre9TNJvgRnNu/tct9UyTuHDyg4W/7E/1a2cnVBXf4sNT931f4Ht72Hnolth4IGwpSuwDiU4sO52eCpWY8vI56QyLWv866cId60Btv+uDIsibpXUtkus+2SQc3cQH2z8cmyI5+5oSGLWJRknpty6Q/Vgl3HSOSjiaXdn9mD1d524c+9PsHa6B2WTs7H+ixI4frcQ56qHYGlhliZ4kasMX3N8Gcue+BR5zm2dBPt1R73is+5gU/rBxi/XOuI5Pp+9vqSKZNyXaMZnX4Ndxv0agzIwIjdg2OQCvPHvqzHK+jqqLtyK2avmA956VNeOiOCc8L3Q7+On1RNQWv8vSe2cDIxMaFRCgBAgBAgBQqB7CCThDEr3ABiMtQebVz7Y+OU6TTwn/5NNMiYZJyMCar1OwhmUZBQZ8UQIEAKEACFACAwuBMhBGVzyJm4JAUKAECAECIGEQIAclIQQExFJCBAChAAhQAgMLgTIQRlc8iZuCQFCgBAgBAiBhECAHJSEEBMRSQgQAoQAIUAIDC4EyEEZXPImbgkBQoAQIAQIgYRAIGybcUJQTUQSAoQAIUAIEAKEQFIiIJ9oP1TNnZypzqM0IUAIEAKEACFACBACsUaAlnhijTiNRwgQAoQAIUAIEAJdIvD/Ab5/wiEui3PVAAAAAElFTkSuQmCC"></p>
<p style="text-align: left;">The relationship between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span> can be modelled by the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = ax + b">
  <mi>y</mi>
  <mo>=</mo>
  <mi>a</mi>
  <mi>x</mi>
  <mo>+</mo>
  <mi>b</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
  <mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation to estimate the BMI of an adult man whose waist size is 95 cm.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A company produces bags of sugar whose masses, in grams, can be modelled by a normal&nbsp;distribution with mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math> and standard deviation <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>5</mn></math>. A bag of sugar is rejected for sale if&nbsp;its mass is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>995</mn></math> grams.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a bag selected at random is rejected.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the number of bags which will be rejected from a random sample of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> bags.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that a bag is not rejected, find the probability that it has a mass greater than&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1005</mn></math> grams.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>There are three fair six-sided dice. Each die has two green faces, two yellow faces and two red faces.</p>
<p>All three dice are rolled.</p>
</div>

<div class="specification">
<p>Ted plays a game using these dice. The rules are:</p>
<ul>
<li>Having a turn means to roll all three dice.</li>
<li>He wins $10 for each green face rolled and adds this to his winnings.</li>
<li>After a turn Ted can either:<br>
<ul>
<li>end the game (and keep his winnings), or</li>
<li>have another turn (and try to increase his winnings).</li>
</ul>
</li>
<li>If two or more red faces are rolled in a turn, all winnings are lost and the game ends.</li>
</ul>
</div>

<div class="specification">
<p>The random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="D">
  <mi>D</mi>
</math></span> ($) represents how much is added to his winnings after a turn.</p>
<p>The following table shows the distribution for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="D">
  <mi>D</mi>
</math></span>, where $<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
  <mi>w</mi>
</math></span> represents his winnings in the game so far.</p>
<p style="text-align: center;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAaoAAABuCAYAAAB2gVfgAAAbqElEQVR4Ae2dD1BU173Hv6w8a60opdp6V61UCGgriRGedowvWSQucWxSK1XzTAWDzWijSSY8hAfRTlKMSYTBmMY01dkNSGKrEZ6aZ1QMSPswqcyusdEGl64JJrCXjg7hz8Younve3GWX3b27wILs3ru7P2aYvffcc8/5nc/vd+7v3vM3gjHGQH9EgAgQASJABGRKQCFTuUgsIkAEiAARIAI2AuSoyBCIABEgAkRA1gQiHdJFREQ4DumXCBABIkAEiIDkBBw9U32OSpDIESi5dGEmgPCSEO7siQFADIiB8OgjO/BkQE1/YeYUqbhEgAgQgWAjQI4q2DRG8hIBIkAEwowAOaowUzgVlwgQASIQbATIUQWbxkheIkAEiECYESBHFWYKp+ISASJABIKNADmqYNMYyUsEiAARCDMC5KjCTOFUXCJABIhAsBEgRxVsGiN5iQARIAJhRoAcVZgpnIpLBIgAEQg2AqHnqKw89OUvoqT2mosurOiq/S1+pr0Eq0souupQUliFJrNbqGsMOiYCRIAIEAGJCUjvqG7rURIfYVs2RFg6xO1fmYWSQ+9Dz/f4hsnaitotL+BgVAY2LJoIwApzUy20+UswIa0Ix9bNwtSsnTjV1NWb3vgFeGwZjxczilDrax6+SUKxgoZAD3h9BfJTlYiISELWzjPgQ/69pQtNtUdwqCQL8fm1sNcGd43ZXvjykSrUSWUWdjbw7i957rGD68zchFMlWVDanjdKpOZXeH/GhDID9IBv2I0spfDMFRj088IuFwbCflTCX+9Sf/aTQP9YGplGzTFgPas03erN3WJiusN7WJ6KY+CymaaxcxCpvmK64tUsu7KZWRwxO2tYHqdmBTVfsK9qtrKlmkZ2y1TPSjOzmcbwjT2WhXU3lrHs7DLW2N13pyOFgPxKyj4gJRw8E2kYWFi3rpSpVM+zGtNNxiwtrKZgKVMVn2Xdg4s84jECw+AbZtBks9WZyxgHMC6vhnnWLKEuLWOqgmpmsjBmMVWzAtUyVqz7asTLLE7Q7wwszexw6R9YtaG31Bbb82A2g6qU6dzqfwgzYBbWfe4wKztrsj0rHQw8bUE+DITFUG1/fjcQR0befh2OSq1hBpGvsLRUsmwOXgzJPSGLQcPUbvdbWGdNAeO4AlbTeYt12h2VkLzFcIId7nNUQjpC5V3N1JpGp5NzT96vZ5Ky92vJfE9cEgY2u1vA8mquOgW1vdyscHmRcV7y91FAGdjrnOfDSagfGqa21RtHZbTXJbf65R8a/mZgMdaz0y033YS3lRfJbnYQygyY5TN2+vQXLs8612elQ+fysgPpm/6ERoN/fYq/VPOIW3wPZogkUky5H4+tSQbq3sHBhvZ+mhiuoU6jAVYtQLzofvDvofzQP9DtcqciIR0/TxjjEjIG8QvTgC37UNcV8u0+LuUO70Or8UMcqJ6CxKnjnCDG3430Na04UN8cOk1dztL5cHQDxvoTqE6Kx9RxjsqkwPiUB7HmwgnUG2/4kIZ8oyji7oNqymg3ARWTYzGHcw0KbQZQ/Agq1TQ4tAv0oK35ChJzlmHeeEeovBg4pHLVUoCPrehq1OEUkpExdzrc9h2xSTIGEyZFAehAW8c33mXr+gQnK6Zg1cJYF/gKjFdtxNsFSuxbtwQri/7P+732UEX8AqxK+gtO6vpzhgPeHsQXzdCXpNr7BpVIdx1wYr2CqnW/QIneDOAGmrQrERGxEtqm4H5Y9SrLXhG5eMROdn9wATdRfeBDGMPxncXajPoD9eDmxGKyx9OhPnQd+NifYn7i+F7TCCcG5ibUan+HF41rsT9nHvpe2WTGwMMUA//EbYfuZDV4pGD+rOhhZG9Fl+4DVMDLA0cxBYu2leFs6WJ8XleHY+ueQUHVJQiPXe9//8L55mth9iY9Dsm5p8E6a5DH8bhgMNn59KD1cDE2ab/E1U7BMY1BwsrfQpN5C+3dt73jC6pQM1oMnwFuXw5BVQD/CGs2wXABSEpUOh9a/slJJqkKz486nN+QCbXjSyssGAgjoQuhjEpE2rqXsO+j0/jI6DKsRmYMpHdU1mtoPm8C1PMw+wee31PCm3znVaHhLhqTo7/txbiFz1YjeC9XbEEKDvOefQuXagrAoRo7MlZgo/aip7NSTETsnGiXB3V/CYZo+Pi7MH9xHPjzzWgTviTMF/D+kX+4f8mOjQQiU5GaODZEIVCxwo6AWYc95ROxfUNKmDhmh4YVGL9oO0zsJky6fchDGTJUhahq9XGEtSOZAP1K7qh6+wkAtbf+JQGCrVlPD3BqpKfE3AGWSMzdU42PSufi1Lq1KHKbZ+VMtu9B7QwK0qPb4Ks2uA/3Fw//F87jS6C3fSB9F9OTpgGX29Ft7YD+oAFzn9uIxbiOto6vYYXwhXUYnU9mIrmv7yJI0djEHoepiTOAC0a00Dw6pyLHKZGYhDB5YeuAfu9xxBSsdbfpsGIwGlzyGrz0x21Q83/DWYP9q0pmDCR2VFaYW4y4ACXmxE506V9y1JsO6PeUYgc/G9mvr4eqr6PPcX2Iv6OmYd4zBdimNqHi5Cde5494b5sfYj6yiB4Jbvmbti3uhdkH/f4bc5Fs+5CNRFTMJOCyEZ//9QiORN+He6ME8+Bxuf1r3G49jt1XFuGJ5OE0z8oCiEgIYQDNQ1CLQmH7wu/o/8VJHD/UzhWxWLhqoUeprG3NOM8vFPUDe0QLooAetB75My4ueRbZM+19Uw7pw4aBo8CArY9e/S2XAHnZgcSOyt4/5fVrqQd87S7kbj4HVUEpti2b7sWRCVxHY3JsPNwG7dhw30BT+V7Ueh3FN7afNvhv9RPu1F/oHkUiKlr4YtVh7wffw3qB96TpSIoDrvN/Q/luHhlPhFbziNcBNLa2+bkh9EAeqsX2OvCkig+g66s79hdK9UNYGO86WnaoacslvvBs0eJg1MNY0+ekunCpvMI+6jccGIh0Idj95XudA0ogLwYSOiorzJeOobxCDyxOwSzH15IwE/rIIWjzH4Yy7RB+WPou9m9bDK5fSe1DZ2FEc5uofdVSh6IX33GZdd6BpsP7UHHhIaxPn+Hu+Gxv0ujny06k1FA+5X6K9RvVmOLCm//TOYzKXO3ePBIKDBQJWLn9l2go2t27MomwssnLpWjIycVKt+kLoVBY38ugSFiO7TmNKHq5xrZKh5WvwctFjcjZvhwJLnbhe4pyitmFpqrnsTrtN8hJm4pRfc3hEzBr/y0o7c3aoczA2lqFdcp05Jc39K7CYrP7N9FWuME5oASArBg4Zr75e6KdI5/e3y9YZWacbTUMIV+Pfy6TFb97jOmE1QJ8+rvKavIWeJmw28kMNX9mxZmz+/LgMkv7ZqW7Ju05wc/1qn+PA8u+v7LcYqbKjSKGgp6WsYKaFpfJgf3df2fh0jG4yUxnX2eZwqRyqFle2Vnbagx3Vprh3R0YBvbJnW71zssEZ4uJnS3NtK1eAVUeK9P1rmIwvJL5fpd/GdxkLZUbe8vkVn5B95zI9oWVAUKRAWOs+wLTuD0Ti1llf/qVCYMIwYSE9x1hjT37oZxef3yWxdqkxZKngN8fz/by1icMxXweq5tX42j2TPcvKVsOwhyhdXgKW3Hc63WfxRhWxGBnP6xCi24iBsFfB0UqHdYp2QHZgWA4YjsIGUclTAjWl2zEazEF2J09e0hDTYVP4Seyr+DJymckad4SK2VYNTzIbyIGnpUzyFU6LPHJDsgOBMMR20HQtzg7a0M0knN2IMv4O+/zpJwRXY6E1dWrUFDYiMfKNkripFyEoUMiQASIABHwQiCEvqgcpRM6S9/A0ehfI9e21Ycj3MuvsB/Vy18i9alVSObEy+h4ie+nIPHbg5+ykXWyxMDzLVLWCvOTcGQHZAeCaYntIAQdlZ9qkB+TFSvFj1nJNmli4Fk5ZassPwpGdkB2IJiX2A5CqOnPj7WHkiYCRIAIEAHJCJCjkgw9ZUwEiAARIAK+ECBH5QslikMEiAARIAKSESBHJRl6ypgIEAEiQAR8IUCOyhdKFIcIEAEiQAQkI0COSjL0lDERIAJEgAj4QsBteLovN1AcIkAEiAARIAKBIOBY1s9tS11HYCAEoDycBMRzBpxXwueIGHjOHQkf7TtLSnZAdiBYg9gOqOnPWUfoiAgQASJABGRIgByVDJVCIhEBIkAEiICTADkqJws6IgJEgAgQARkSIEclQ6WQSESACBABIuAkQI7KyYKOiAARIAJEQIYEyFHJUCkkEhEgAkSACDgJkKNysqAjIkAEiAARkCEBclQyVAqJRASIABEgAk4C5KicLOiICBABIkAEZEiAHJUMlUIiEQEiQASIgJMAOSonCzoiAkSACBABGRIgRyVDpZBIRIAIEAEi4CRAjsrJgo6IABEgAkRAhgTIUclQKSQSESACRIAIOAmQo3KyoCMiEKYEutBUewSHSrIQn1+LrrCj0IWmUzuRpYywbS8RkZqPcj0PazhykKkdkKMKO2OkAhMBVwI30KR9Fi+Ul+Hpzftw3fVSWBz3oPVIBY5hKXabGJjFhLOPtKEg5QmU6jvCgkBvIeVtB247/NLGidLYpXiTMGmkkDZXYuC5WVxANWK9BO2SRdgy521cemURxgc0c2dmAbcD6+eo+2sk7ldNQ99bu8QsAs7AiR+QuOwOUcQM3Hb4dUSiXyJABIhAWBBQ/AgqlaikiomInaMUBdKplAT6XiKkFILyJgJEgAjIi8D3sGR+HMbJS6iwlYYcVdiqngpOBIiAVwJdn+Dk+YfwpNqlOdBrRAoMFAFyVIEiTfkQASIQBAQ6oN9zFJO2P47kcfR4lIvCSBNy0QTJQQSIgMQErDDr/4yDMb/GhuRoiWWh7F0JkKNypUHHRIAIhC0Ba+sJ7L24EFuzZ1PflMysgByVzBRC4hABIhB4Ala+FrsOjsGjaxxOygrzpUPQ1l0LvDCUowcBclQeSCiACBCB8CFghbmpCgWrf4WcnDQoR9lXp4gYhahZBwEljfuTgy2Qo5KDFkgGIiAZASu6aguhHDUL66p58DvSMCFiJbRNNySTKJAZW1sP4xlVBnbU8Z7Zqh/CwvgxnuEhGSJvO6CVKXw0utv6EsxM2YzL4KDW1OJ49kznTHYf0+gvmngWdn/xQjmcGEi8MoVMjIvsgOxAMEWxHYzIF5W1SYv0CMcns+tvErJKDqC2yZdlLrvQVPUaSqouwWyrNGboS1J7F4n0SFtIdz+OBHDhyMjkXDQZNFDjB/ih4RB2nWqyyymTGk5iEAEiQARClMCIOCpFQjZOsm9g0KwA1BoYLAyMWdBteAGTjz2LNNWz0F4awFlZW1FbWIij0zORu3ymfcTNOCTnHu9NE3HIrPwCwlqEjN2ESfcSHrhajmUpajyuvRggh3EDxvoTqOaW4D+fy8Wjo97FxsJT4MNvieUQrQpULCJABORKYEQclffCKTAuYTle+uM2qHkttryl62f7gA7oSzehKCZzgLkLc/HA7En2bEaDS/4Zsl/ag8psYN+6/8abAVnl2IwWw2dAUjymjhsDbtFGPB3zBlaXNgTIUXqnTKFEgAgQgVAn4EdH1YtOMTkWcziAP9+MNo+vD2GC3VvI3fxvWPPI3V7mLlzFxb+cA+Lm4Z4Zok5NxTQ8+NjD4HAMpQfP9eMER1B9t6/gXKUJ6lULEG+jFo17H3kYozeX4GCYdDyPIE1KiggQASLgMwG/OyprWzPO8wA3JxaTPXJrR8PBd1DX3+iarn/i7KnL4DLm4i6Pdd4VGDshBmMB8G0d+NrnIvsa0XUztXTkv7ofxy4rMSd2Yt8gCsWMe7A47l1s0Xzof0fpq9i+xuOrkOXo+0vdCb3ZCit/BjuzkhARkYoSfW9Poa/JBV+82+CrNtj7QJVILXF8GdtHPyk3oaq1J/iKRRITgRAk4OE67riMF86g3j54Qnjw7XpxJ6qxFDkr53rucSMs/lih78eJWdGl+wAVfBwWz7/L894BBf0SVVnx/QzEcA72iC/R47a3dGx9ZiuQuP0qfl7XCUvLelwrLUUdp0Z6SozzjsjvY8Z9ceArPoCuy+Nz0RlPjkfccpSzm2ip3Aiu7h0crH4Pu179DEt2/x2MnUZucqjPH4kEt/xNMEsjNGqg7tRFmGwqVGDcrFSsTfwKHV8HmU7laGckExEYAQIj76h4LdbNmmBzEqOUC1GMLFTq9iLHy9pZt/95DpU8MHbSBNuXkXt5etDWbAQP1/4p1xhWXO9st+1Iyk2OxndcL2Ealpcb7YMvhAEY3v+Nucnw+FCD0Ge2Hmlld6Hy7eexPGE8FNyPcV8SZ++fckX2XUxPmgbwRjS3BePb92hMeXA51nB67Nh0CtOfXoWZ4bYQp2Iq7lmcCFxuR7fdLyl+MA3xM+bjHuVoN6sKtRNhCLAv/6FWbkd5fCm7axzHfcH661qWkToOFAvXp+7I5Nk36q/XOZjKc7E8metrLvM5E2sz6g/UA/01C6IdupPV4JGMNel3D/GLq38prE1VKNx8Duptm7BsSu+Dysp/ijMX4NI/Jb7/Ktq7vX6biSPK73z83UhfkwwkzcVsLrQfzN7hRyIqZhJw2YgrVwUd9qD18FtoWPpz3BviTru/FzhxuHduwR8qLudg58Fe4sHKN5zrgWIy8o5qpCQ3m2C4wPfbLGjWV6Bohx5cdiGeVk0U5Trcpj/HEPS1yP9lgt25duDjP2mh5d37p0QZBu+p9Wt0XLsJVJ9AvTE8ViNwV1YkoqJdmnPN53FQtwBbl00f+suVe8J0RgSIwAgRkKmjcvRPef9asvI12J5bjDrV83h7288wxaMUw236s48yHBuDCWOFRB2jEo8B4v4pNwVMQkyUZyOiWxRZnghfD2/g2MQHoMJnMLSE+gAKb0pQ4DvRMeBgwGdfGlG74xSmb1zixaa83UthRIAIBIKAxyN++JneQHf7daCnE93XfeuEjrxrLjI44PrVTltfU1/e5k9xqPw98EjB/FmOfWF6wOvfR5U2H2lKNcp++BzO7i/AohFtrvo2oidHA9ebceVfZvANe1B0JAZrcoSmse+g+dD7aHIr2g10Xu0GuHjETg6+ZjNr6/+iqHo+fvfiJqxRm1Bx8mO06t9EYdUVuBWzTzGheOAYPXoNH+9+E3WqtX1NvqFYWioTEQhKAsz+BwhjDob3ZzFomBpgQhq9/xxTaxqZZdDkrrKavGQGtYYZbJFvMVPlepd0HOk5fmezzOJ32GGdyYe0B83cSwQL624sY5mckJ+a5ZWdZSbLF6wyM46By2aaxk73eyyNTKPmGJdXw0RX3OMNcnYn7AdJ2uvlW7piFgeOqfIqmaFbAP8V0xUv7S1zZSPr9nqXfwMDzcC1NL32O5tlai5IUnaHLFIycMgg9S8xYLbnn9R6kDp/sR1IviitsE7gksQTWGXYh+wE0aRembv+kZJdGIEjdGSG85+UDKxN5XiiTIlt2xaDG8E2hqHqU0oGQ5XVX/GJgeeCrP5iLed0xXYgYbXsxaRIWI7txbdQcfSTIFuKqAMfH30PPcW5WBlkDlbOBhpw2cwN2KVRYHNhmqROKuDlds3QyqNhZxaUtuHq6cjvWxjaNVIoHwvdChXIT1Xahusrs3bilE8LaQcrE2EPrpMosU3uF6YopCO/vEG0bql94rvXKQyB3wZGckcFRCM553Vsbddie21rkPSN9ICv3Y3X2p/E/px5XpZ+ClYDDhO5zQ0oSb0P/6U9hJ1F53D/1sfCb/5Yn6o78PHhM8Cje2ESFnw++wjaNv0KRbXhsrOtMGBqN9a+1oWM/c1grBO1D1xElqowZFcmsbaewN5jwCO2yf12nRcsE61b6pj+02cozoN+pww5o4z4kaMtUtwm6AgP3G8nM1TuYsUS9ZH4Xs6Rl1N69r6X3l8xA8qgs4blcUIf3T6mM930V5GGnG5AGdilsxjr2ekWVwa9/cZ32u865MLbbwg4A1s/8wKWV3PVKbKlmVVmz77jvmdngkM78i+Db5jx9EesxW0AwTfMoFnBwBWwmk77hc7TrHhrNTO5xbOwzpqtbKlP4w+GVmZxbDEDyfuoRtzzBmGC4vbYICzCHYtMDGTSN2G9BO2SArRvfwu5XlaTuWNFD5JAoO3Aez/zDTRpM5G4JR41l7Zh0fjANjwFmoEwDaerdgtm/gp4215eK38Zn0f9CHGuk95ttlEE/F7j9/EEYgaB1cAgRkqXiQARkIqA0G9RC23BqzDmv+51yTOpJPNfvlaYW4y44JHBaEyOjQcXtEujeRTIp4CxS1KQaHdMCi7O3UkJs0qNH6JqagbS4wM/6I0clU8qpEhEIJQJXENt/jxEJaZh3Y6j+OjkWRjN4TCTToFxU+ORhHocqG/27B8P0vmRQ7dUoT+qFRueXDTARHdh1Z4G/OSx+weIM/Scfb2DHJWvpCgeEQhZAhOx6BUdmMUEXdkaYEcGVM8cRmsY+CpFwiPIz1Oieksxyuy7kFt5Hf7npB68bZPUUH9ECoNJ9qN80sYBNq4VPqeaUV/1fffdIwJYH0JdCwFESVkRgSAnoOCQnPUC/qhZAf64Doaw+KqaiEVb96M65za2CLs+KLNQeubv+LTh8gCLUAe5nl3FN+uw9+B3UbAhZcDRy7Zmv5+okBLg/jqHqOSoHCTolwgQAQBjEL/wIajDicW4BCzOLYdJ2A7IVI6cu0fhvGGly8LUIQrDegVH9n6OJYNOz7A3+43gLhVDJUqOaqjEKD4RCGkCvQMMLrt0rId0cUWFs/KnsGX9e1j8Xl7AR/uJRPHvqbA57K7jiHr0F845hOaLKNee8dytXOJmPwEEOSr/mgOlTgRkTKAHrVWboEzNR7metw0mEHYmePmVdhRuflCSTnPJYJmbUHuoBI//x9uY9MoboT3q0XwJVQXZSMv5DdKU33Junhmlxn58z6MJUOpmP8EmyFFJVjMoYyIgNYFITPjxv2OxYQfWpigxKiIJj7/TjYyy15A9c7zUwgUm/65a5CsjEBH1FE52zcVz59/Cs/OGsdFrYKS981ysV1D1zApk7Kj2ktZCrFoYK3IKQrOfAaqVc0dsc1ovGQ8aRBN+B0Xk/wjiyW3+z1F+ORADmUz4ldg0yA7IDgQTFNsBfVFJXDEpeyJABIgAERiYADmqgfnQVSJABIgAEZCYADkqiRVA2RMBIkAEiMDABMhRDcyHrhIBIkAEiIDEBMhRSawAyp4IEAEiQAQGJkCOamA+dJUIEAEiQAQkJkCOSmIFUPZEgAgQASIwMAFyVAPzoatEgAgQASIgMQFyVBIrgLInAkSACBCBgQmQoxqYD10lAkSACBABiQmQo5JYAZQ9ESACRIAIDEyAHNXAfOgqESACRIAISEyAHJXECqDsiQARIAJEYGAC5KgG5kNXiQARIAJEQGICbtt8SCwLZU8EiAARIAJEoI8AY8x2HOkIcQQ4zumXCBABIkAEiIAcCFDTnxy0QDIQASJABIhAvwT+H3GUUSGr0zT3AAAAAElFTkSuQmCC"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of rolling exactly one red face.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability of rolling two or more red faces.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that, after a turn, the probability that Ted adds exactly $10 to his winnings is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{1}{3}}">
  <mrow>
    <mfrac>
      <mn>1</mn>
      <mn>3</mn>
    </mfrac>
  </mrow>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Ted will always have another turn if he expects an increase to his winnings.</p>
<p>Find the least value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="w">
  <mi>w</mi>
</math></span> for which Ted should end the game instead of having another turn.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The length, <em>X </em>mm, of a certain species of seashell is normally distributed with mean 25 and&nbsp;variance, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\sigma ^2}">
  <mrow>
    <msup>
      <mi>σ<!-- σ --></mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span>.</p>
<p>The probability that <em>X</em> is less than 24.15 is 0.1446.</p>
</div>

<div class="specification">
<p>A random sample of 10 seashells is collected on a beach. Let <em>Y</em> represent the number of&nbsp;seashells with lengths greater than 26 mm.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find P(24.15 &lt; <em>X</em> &lt; 25).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sigma ">
  <mi>σ</mi>
</math></span>, the standard deviation of <em>X</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the probability that a seashell selected at random has a length greater than 26 mm.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find E(<em>Y</em>).</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that exactly three of these seashells have a length greater than 26 mm.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A seashell selected at random has a length less than 26 mm.</p>
<p>Find the probability that its length is between 24.15 mm and 25 mm.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question">
<p>Events <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> are independent and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mn>3</mn><mtext>P</mtext><mo>(</mo><mi>B</mi><mo>)</mo></math>.</p>
<p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>A</mi><mo>∪</mo><mi>B</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>.</mo><mn>68</mn></math>, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>P</mtext><mo>(</mo><mi>B</mi><mo>)</mo></math>.</p>
</div>
<br><hr><br><div class="specification">
<p>The following table below shows the marks scored by seven students on two different&nbsp;mathematics tests.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Let <em>L</em><sub>1</sub> be the regression line of <em>x</em> on <em>y</em>. The equation of the line <em>L</em><sub>1</sub> can be written in the&nbsp;form <em>x</em> = <em>ay</em> + <em>b</em>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>a</em> and the value of <em>b</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <em>L</em><sub>2</sub> be the regression line of <em>y</em> on <em>x</em>. The lines <em>L</em><sub>1</sub> and <em>L</em><sub>2</sub> pass through the same point with coordinates (<em>p</em> , <em>q</em>).</p>
<p>Find the value of <em>p</em> and the value of <em>q</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Contestants in a TV gameshow try to get through three walls by passing through doors without falling into a trap. Contestants choose doors at random.<br>If they avoid a trap they progress to the next wall.<br>If a contestant falls into a trap they exit the game before the next contestant plays.<br>Contestants are not allowed to watch each other attempt the game.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The first wall has four doors with a trap behind one door.</p>
<p style="text-align: left;">Ayako is a contestant.</p>
</div>

<div class="specification">
<p>Natsuko is the second contestant.</p>
</div>

<div class="specification">
<p>The second wall has five doors with a trap behind two of the doors.</p>
<p>The third wall has six doors with a trap behind three of the doors.</p>
<p>The following diagram shows the branches of a probability tree diagram for a contestant in the game.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that Ayako avoids the trap in this wall.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that only one of Ayako and Natsuko falls into a trap while attempting to pass through a door <strong>in the first wall</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy</strong> the probability tree diagram and write down the relevant probabilities along the branches.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A contestant is chosen at random. Find the probability that this contestant fell into a trap while attempting to pass through a door in the second wall.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A contestant is chosen at random. Find the probability that this contestant fell into a trap.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>120 contestants attempted this game.</p>
<p>Find the expected number of contestants who fell into a trap while attempting to pass through a door in the third wall.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>The principal of a high school is concerned about the effect social media use might be having on the self-esteem of her students. She decides to survey a random sample of 9 students to gather some data. She wants the number of students in each grade in the sample to be, as far as possible, in the same proportion as the number of students in each grade in the school.</p>
</div>

<div class="specification">
<p>The number of students in each grade in the school is shown in table.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>In order to select the 3 students from grade 12, the principal lists their names in alphabetical order and selects the 28<sup>th</sup>, 56<sup>th</sup> and 84<sup>th</sup> student on the list.</p>
</div>

<div class="specification">
<p>Once the principal has obtained the names of the 9 students in the random sample, she surveys each student to find out how long they used social media the previous day and measures their self-esteem using the Rosenberg scale. The Rosenberg scale is a number between 10 and 40, where a high number represents high self-esteem.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the name for this type of sampling technique.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that 3 students will be selected from grade 12.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of students in each grade in the sample.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the name for this type of sampling technique.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate Pearson’s product moment correlation coefficient, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret the meaning of the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span> in the context of the principal’s concerns.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span> makes it appropriate to find the equation of a regression line.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Another student at the school, Jasmine, has a self-esteem value of 29.            </p>
<p>By finding the equation of an appropriate regression line, estimate the time Jasmine spent on social media the previous day.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>A healthy human body temperature is 37.0 °C. Eight people were medically examined and the difference in their body temperature (°C), from 37.0 °C, was recorded. Their heartbeat (beats per minute) was also recorded.</p>
<p><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a scatter diagram for temperature difference from 37 °C (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>) against heartbeat (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span>). Use a scale of 2 cm for 0.1 °C on the horizontal axis, starting with −0.3 °C. Use a scale of 1 cm for 2 heartbeats per minute on the vertical axis, starting with 60 beats per minute.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean temperature difference from 37 °C, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
  <mrow>
    <mover>
      <mi>x</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for this set of data the mean number of heartbeats per minute, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar y">
  <mrow>
    <mover>
      <mi>y</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot and label the point M(<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar x">
  <mrow>
    <mover>
      <mi>x</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\bar y">
  <mrow>
    <mover>
      <mi>y</mi>
      <mo stretchy="false">¯</mo>
    </mover>
  </mrow>
</math></span>) on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the Pearson’s product–moment correlation coefficient, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence describe the correlation between temperature difference from 37 °C and heartbeat.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to find the equation of the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the regression line <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y">
  <mi>y</mi>
</math></span> on <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span> on the scatter diagram.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 66 people went on holiday to Hawaii. During their stay, three trips were arranged: a boat trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
  <mi>B</mi>
</math></span>), a coach trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
  <mi>C</mi>
</math></span>) and a helicopter trip (<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
  <mi>H</mi>
</math></span>).</p>
<p>From this group of people:</p>
<table style="width: 691.333px;">
<tbody>
<tr>
<td style="width: 182px; text-align: right;">3&nbsp;</td>
<td style="width: 526.333px;">went on all three trips;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">16&nbsp;</td>
<td style="width: 526.333px;">went on the coach trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">13&nbsp;</td>
<td style="width: 526.333px;">went on the boat trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">5&nbsp;</td>
<td style="width: 526.333px;">went on the helicopter trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;"><em>x&nbsp;</em></td>
<td style="width: 526.333px;">went on the coach trip and the helicopter trip <strong>but not</strong> the boat trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">2<em>x&nbsp;</em>
</td>
<td style="width: 526.333px;">went on the boat trip and the helicopter trip <strong>but not</strong> the coach trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">4<em>x&nbsp;</em>
</td>
<td style="width: 526.333px;">went on the boat trip and the coach trip <strong>but not</strong> the helicopter trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">8&nbsp;</td>
<td style="width: 526.333px;">did not go on any of the trips.</td>
</tr>
</tbody>
</table>
</div>

<div class="specification">
<p>One person in the group is selected at random.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a Venn diagram to represent the given information, using sets labelled <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="B">
  <mi>B</mi>
</math></span>, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="C">
  <mi>C</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="H">
  <mi>H</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 3">
  <mi>x</mi>
  <mo>=</mo>
  <mn>3</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="n(B \cap C)">
  <mi>n</mi>
  <mo stretchy="false">(</mo>
  <mi>B</mi>
  <mo>∩</mo>
  <mi>C</mi>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this person</p>
<p>(i) &nbsp; &nbsp; went on at most one trip;</p>
<p>(ii) &nbsp; &nbsp; went on the coach trip, given that this person also went on both the helicopter trip and the boat trip.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the mean weight, <em>y</em> kg , of children who are <em>x</em> years old.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">The relationship between the variables is modelled by the regression line with equation&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = ax + b">
  <mi>y</mi>
  <mo>=</mo>
  <mi>a</mi>
  <mi>x</mi>
  <mo>+</mo>
  <mi>b</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of<em> a</em> and of <em>b</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the correlation coefficient.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your equation to estimate the mean weight of a child that is 1.95 years old.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Ten students were surveyed about the number of hours, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
  <mi>x</mi>
</math></span>, they spent browsing the Internet during week 1 of the school year. The results of the survey are given below.</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\sum\limits_{i = 1}^{10} {{x_i} = 252,{\text{ }}\sigma &nbsp;= 5{\text{ and median}} = 27.} ">
  <munderover>
    <mo movablelimits="false">∑<!-- ∑ --></mo>
    <mrow>
      <mi>i</mi>
      <mo>=</mo>
      <mn>1</mn>
    </mrow>
    <mrow>
      <mn>10</mn>
    </mrow>
  </munderover>
  <mrow>
    <mrow>
      <msub>
        <mi>x</mi>
        <mi>i</mi>
      </msub>
    </mrow>
    <mo>=</mo>
    <mn>252</mn>
    <mo>,</mo>
    <mrow>
      <mtext>&nbsp;</mtext>
    </mrow>
    <mi>σ<!-- σ --></mi>
    <mo>=</mo>
    <mn>5</mn>
    <mrow>
      <mtext>&nbsp;and median</mtext>
    </mrow>
    <mo>=</mo>
    <mn>27.</mn>
  </mrow>
</math></span></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the mean number of hours spent browsing the Internet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During week 2, the students worked on a major project and they each spent an additional five hours browsing the Internet. For week 2, write down</p>
<p>(i) &nbsp; &nbsp; the mean;</p>
<p>(ii) &nbsp; &nbsp; the standard deviation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>During week 3 each student spent 5% less time browsing the Internet than during week 1. For week 3, find</p>
<p>(i) &nbsp; &nbsp; the median;</p>
<p>(ii) &nbsp; &nbsp; the variance.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The following table shows the systolic blood pressures, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> mmHg, and the ages, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> years, of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math> male patients at a medical clinic.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The relationship between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> can be modelled by the regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> with&nbsp;equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a</mi><mi>t</mi><mo>+</mo><mi>b</mi></math> .</p>
</div>

<div class="specification">
<p>A <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math>‐year‐old male patient enters the medical clinic for his appointment.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the value of Pearson’s product‐moment correlation coefficient, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, for these data.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Interpret, in context, the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math> found in part (a) (i).</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the equation of the regression line of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation from part (b) to predict this patient’s systolic blood&nbsp;pressure.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math>‐year‐old male patient enters the medical clinic for his appointment.</p>
<p>Explain why the regression equation from part (b) should not be used to predict this&nbsp;patient’s systolic blood pressure.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A nationwide study on reaction time is conducted on participants in two age groups. The participants in Group X are less than 40 years old. Their reaction times are normally distributed with mean 0.489 seconds and standard deviation 0.07 seconds.</p>
</div>

<div class="specification">
<p>The participants in Group Y are 40 years or older. Their reaction times are normally distributed with mean 0.592 seconds and standard deviation <em>σ</em> seconds.</p>
</div>

<div class="specification">
<p>In the study, 38 % of the participants are in Group X.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A person is selected at random from Group X. Find the probability that their reaction time is greater than 0.65 seconds.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The probability that the reaction time of a person in Group Y is greater than 0.65 seconds is 0.396. Find the value of <em>σ</em>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A randomly selected participant has a reaction time greater than 0.65 seconds. Find the probability that the participant is in Group X.</p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Ten of the participants with reaction times greater than 0.65 are selected at random. Find the probability that at least two of them are in Group X.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>SpeedWay airline flies from city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
  <mrow>
    <mtext>A</mtext>
  </mrow>
</math></span> to city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
  <mrow>
    <mtext>B</mtext>
  </mrow>
</math></span>. The flight time is normally distributed with a mean of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="260">
  <mn>260</mn>
</math></span> minutes and a standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="15">
  <mn>15</mn>
</math></span> minutes.</p>
<p>A flight is considered late if it takes longer than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="275">
  <mn>275</mn>
</math></span> minutes.</p>
</div>

<div class="specification">
<p>The flight is considered to be <strong>on time</strong> if it takes between <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
  <mi>m</mi>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="275">
  <mn>275</mn>
</math></span> minutes. The probability that a flight is on time is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.830">
  <mn>0.830</mn>
</math></span>.</p>
</div>

<div class="specification">
<p>During a week, SpeedWay has <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="12">
  <mn>12</mn>
</math></span> flights from city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}">
  <mrow>
    <mtext>A</mtext>
  </mrow>
</math></span> to city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}">
  <mrow>
    <mtext>B</mtext>
  </mrow>
</math></span>. The time taken for any flight is independent of the time taken by any other flight.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability a flight is <strong>not</strong> late.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m"> <mi>m</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the probability that at least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7"> <mn>7</mn> </math></span> of these flights are <strong>on time</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that at least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="7"> <mn>7</mn> </math></span> of these flights are on time, find the probability that exactly <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="10"> <mn>10</mn> </math></span> flights are on time.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>SpeedWay increases the number of flights from city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{A}}"> <mrow> <mtext>A</mtext> </mrow> </math></span> to city <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B}}"> <mrow> <mtext>B</mtext> </mrow> </math></span> to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="20"> <mn>20</mn> </math></span> flights each week, and improves their efficiency so that more flights are on time. The probability that at least <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="19"> <mn>19</mn> </math></span> flights are on time is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="0.788"> <mn>0.788</mn> </math></span>.</p>
<p>A flight is chosen at random. Calculate the probability that it is on time.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The mass <em>M</em> of apples in grams is normally distributed with mean <em>μ</em>. The following table shows probabilities for values of <em>M</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="specification">
<p>The apples are packed in bags of ten.</p>
<p>Any apples with a mass less than 95 g are classified as small.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>k</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <em>μ</em> = 106.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <em>P</em>(M &lt; 95) .</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a bag of apples selected at random contains at most one small apple.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected number of bags in this crate that contain at most one small apple.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that at least 48 bags in this crate contain at most one small apple.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Two events <em>A</em> and <em>B</em> are such that P(<em>A</em>) = 0.62 and P<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\left( {A \cap B} \right)">
  <mrow>
    <mo>(</mo>
    <mrow>
      <mi>A</mi>
      <mo>∩<!-- ∩ --></mo>
      <mi>B</mi>
    </mrow>
    <mo>)</mo>
  </mrow>
</math></span> = 0.18.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find P(<em>A</em> ∩ <em>B′ </em>).</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that P((<em>A</em> ∪ <em>B</em>)′<em> </em>) = 0.19, find P(<em>A </em>|<em> </em><em>B</em>′<em> </em>).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A bakery makes two types of muffins: chocolate muffins and banana muffins.</p>
<p>The weights, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> grams, of the chocolate muffins are normally distributed with a mean of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>62</mn><mo>&#8202;</mo><mtext>g</mtext></math>&nbsp;and standard deviation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>9</mn><mo>&#8202;</mo><mtext>g</mtext></math>.</p>
</div>

<div class="specification">
<p>The weights, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> grams, of the banana muffins are normally distributed with a mean of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>68</mn><mo>&#8202;</mo><mtext>g</mtext></math>&nbsp;and standard deviation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>4</mn><mo>&#8202;</mo><mtext>g</mtext></math>.</p>
<p>Each day <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>%</mo></math> of the muffins made are chocolate.</p>
<p>On a particular day, a muffin is randomly selected from all those made at the bakery.</p>
</div>

<div class="specification">
<p>The machine that makes the chocolate muffins is adjusted so that the mean weight of the&nbsp;chocolate muffins remains the same but their standard deviation changes to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#963;</mi><mo>&#8202;</mo><mtext>g</mtext></math>. The&nbsp;machine that makes the banana muffins is not adjusted. The probability that the weight of a&nbsp;randomly selected muffin from these machines is less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo>&#8202;</mo><mtext>g</mtext></math> is now <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>157</mn></math>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that a randomly selected chocolate muffin weighs less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo> </mo><mtext>g</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In a random selection of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math> chocolate muffins, find the probability that exactly <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> weigh less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo> </mo><mtext>g</mtext></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the randomly selected muffin weighs less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo> </mo><mtext>g</mtext></math>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that a randomly selected muffin weighs less than <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61</mn><mo> </mo><mtext>g</mtext></math>, find the probability that it is chocolate.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The number of messages, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="M">
  <mi>M</mi>
</math></span>, that six randomly selected teenagers sent during the month of October is shown in the following table. The table also shows the time, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
  <mi>T</mi>
</math></span>, that they spent talking on their phone during the same month.</p>
<p><img src="data:image/png;base64,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"></p>
<p>The relationship between the variables can be modelled by the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="M = aT + b">
  <mi>M</mi>
  <mo>=</mo>
  <mi>a</mi>
  <mi>T</mi>
  <mo>+</mo>
  <mi>b</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b"> <mi>b</mi> </math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your regression equation to predict the number of messages sent by a teenager that spent <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="154"> <mn>154</mn> </math></span> minutes talking on their phone in October.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A random sample of nine adults were selected to see whether sleeping well affected their&nbsp;reaction times to a visual stimulus. Each adult&rsquo;s reaction time was measured twice.</p>
<p>The first measurement for reaction time was taken on a morning after the adult had&nbsp;slept well. The second measurement was taken on a morning after the same adult had not&nbsp;slept well.</p>
<p>The box and whisker diagrams for the reaction times, measured in seconds, are shown below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">Consider the box and whisker diagram representing the reaction times after sleeping well.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the median reaction time after sleeping well.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Verify that the measurement of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>46</mn></math> seconds is not an outlier.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why it appears that the mean reaction time is greater than the median reaction time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Now consider the two box and whisker diagrams.</p>
<p>Comment on whether these box and whisker diagrams provide any evidence that might suggest that not sleeping well causes an increase in reaction time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A six-sided biased die is weighted in such a way that the probability of obtaining a “six” is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{7}{{10}}">
  <mfrac>
    <mn>7</mn>
    <mrow>
      <mn>10</mn>
    </mrow>
  </mfrac>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The die is tossed five times. Find the probability of obtaining at most three “sixes”.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The die is tossed five times. Find the probability of obtaining the third “six” on the fifth toss.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A group of 800 students answered 40 questions on a category of their choice out of History, Science and Literature.</p>
<p>For each student the category and the number of correct answers, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
  <mi>N</mi>
</math></span>, was recorded. The results obtained are represented in the following table.</p>
<p><img src="images/Schermafbeelding_2018-02-13_om_14.11.54.png" alt="N17/5/MATSD/SP2/ENG/TZ0/01"></p>
</div>

<div class="specification">
<p>A <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
  <mrow>
    <msup>
      <mi>χ<!-- χ --></mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span> test at the 5% significance level is carried out on the results. The critical value for this test is 12.592.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
  <mi>N</mi>
</math></span> is a discrete or a continuous variable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
  <mi>N</mi>
</math></span>, the modal class;</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down, for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
  <mi>N</mi>
</math></span>, the mid-interval value of the modal class.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to estimate the mean of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
  <mi>N</mi>
</math></span>;</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use your graphic display calculator to estimate the standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
  <mi>N</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the expected frequency of students choosing the Science category and obtaining 31 to 40 correct answers.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the null hypothesis for this test;</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p">
  <mi>p</mi>
</math></span>-value for the test;</p>
<div class="marks">[1]</div>
<div class="question_part_label">f.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\chi ^2}">
  <mrow>
    <msup>
      <mi>χ</mi>
      <mn>2</mn>
    </msup>
  </mrow>
</math></span> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the result of the test. Give a reason for your answer.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p>A random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span> is normally distributed with mean, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
  <mi>μ<!-- μ --></mi>
</math></span>. In the following diagram, the shaded region between 9 and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
  <mi>μ<!-- μ --></mi>
</math></span> represents 30% of the distribution.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_10.15.49.png" alt="M17/5/MATME/SP2/ENG/TZ1/09"></p>
</div>

<div class="specification">
<p>The standard deviation of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span> is 2.1.</p>
</div>

<div class="specification">
<p>The random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y">
  <mi>Y</mi>
</math></span> is normally distributed with mean <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
  <mi>λ<!-- λ --></mi>
</math></span> and standard deviation 3.5. The events <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X > 9">
  <mi>X</mi>
  <mo>&gt;</mo>
  <mn>9</mn>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y > 9">
  <mi>Y</mi>
  <mo>&gt;</mo>
  <mn>9</mn>
</math></span> are independent, and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="P\left( {(X > 9) \cap (Y > 9)} \right) = 0.4">
  <mi>P</mi>
  <mrow>
    <mo>(</mo>
    <mrow>
      <mo stretchy="false">(</mo>
      <mi>X</mi>
      <mo>&gt;</mo>
      <mn>9</mn>
      <mo stretchy="false">)</mo>
      <mo>∩<!-- ∩ --></mo>
      <mo stretchy="false">(</mo>
      <mi>Y</mi>
      <mo>&gt;</mo>
      <mn>9</mn>
      <mo stretchy="false">)</mo>
    </mrow>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mn>0.4</mn>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X &lt; 9)">
  <mrow>
    <mtext>P</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mi>X</mi>
  <mo>&lt;</mo>
  <mn>9</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\mu ">
  <mi>μ</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\lambda ">
  <mi>λ</mi>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Y &gt; 9">
  <mi>Y</mi>
  <mo>&gt;</mo>
  <mn>9</mn>
</math></span>, find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(Y &lt; 13)">
  <mrow>
    <mtext>P</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mi>Y</mi>
  <mo>&lt;</mo>
  <mn>13</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A jigsaw puzzle consists of many differently shaped pieces that fit together to form a picture.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>Jill is doing a 1000-piece jigsaw puzzle. She started by sorting the edge pieces from the interior pieces. Six times she stopped and counted how many of each type she had found. The following table indicates this information.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>Jill models the relationship between these variables using the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="y = ax + b">
  <mi>y</mi>
  <mo>=</mo>
  <mi>a</mi>
  <mi>x</mi>
  <mo>+</mo>
  <mi>b</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
  <mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the model to predict how many edge pieces she had found when she had sorted a <strong>total</strong> of 750 pieces.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Ten students were asked for the distance, in km, from their home to school. Their responses are recorded below.</p>
<p style="text-align: center;">0.3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;0.4&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3.5&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;5&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;7&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;8&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;8&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;10</p>
</div>

<div class="specification">
<p>The following box-and-whisker plot represents this data.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For these data, find the mean distance from a student’s home to school.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="p"> <mi>p</mi> </math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the interquartile range.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A jar contains 5 red discs, 10 blue discs and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
  <mi>m</mi>
</math></span> green discs. A disc is selected at random and replaced. This process is performed four times.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that the first disc selected is red.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span> be the number of red discs selected. Find the smallest value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="m">
  <mi>m</mi>
</math></span> for which <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{Var}}(X{\text{ }}) &lt; 0.6">
  <mrow>
    <mtext>Var</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mi>X</mi>
  <mrow>
    <mtext> </mtext>
  </mrow>
  <mo stretchy="false">)</mo>
  <mo>&lt;</mo>
  <mn>0.6</mn>
</math></span>.</p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>In Lucy&rsquo;s music academy, eight students took their piano diploma examination and achieved&nbsp;scores out of 150. For her records, Lucy decided to record the average number of hours per&nbsp;week each student reported practising in the weeks prior to their examination. These results&nbsp;are summarized in the table below.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find Pearson’s product-moment correlation coefficient, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math>, for these data.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The relationship between the variables can be modelled by the regression equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>a</mi><mi>h</mi><mo>+</mo><mi>b</mi></math>. Write down the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> and the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>One of these eight students was disappointed with her result and wished she had practised more. Based on the given data, determine how her score could have been expected to alter had she practised an extra five hours per week.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A discrete random variable <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="X">
  <mi>X</mi>
</math></span> has the following probability distribution.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-12_om_10.34.18.png" alt="N17/5/MATME/SP2/ENG/TZ0/04"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span>.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2)">
  <mrow>
    <mtext>P</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mi>X</mi>
  <mo>=</mo>
  <mn>2</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{P}}(X = 2|X &gt; 0)">
  <mrow>
    <mtext>P</mtext>
  </mrow>
  <mo stretchy="false">(</mo>
  <mi>X</mi>
  <mo>=</mo>
  <mn>2</mn>
  <mrow>
    <mo stretchy="false">|</mo>
  </mrow>
  <mi>X</mi>
  <mo>&gt;</mo>
  <mn>0</mn>
  <mo stretchy="false">)</mo>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The maximum temperature <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="T">
  <mi>T</mi>
</math></span>, in degrees Celsius, in a park on six randomly selected days is shown in the following table. The table also shows the number of visitors, <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N">
  <mi>N</mi>
</math></span>, to the park on each of those six days.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-08-14_om_17.34.22.png" alt="M17/5/MATME/SP2/ENG/TZ2/02"></p>
<p>The relationship between the variables can be modelled by the regression equation <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="N = aT + b">
  <mi>N</mi>
  <mo>=</mo>
  <mi>a</mi>
  <mi>T</mi>
  <mo>+</mo>
  <mi>b</mi>
</math></span>.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a">
  <mi>a</mi>
</math></span> and of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="b">
  <mi>b</mi>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of&nbsp; <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="r">
  <mi>r</mi>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the regression equation to estimate the number of visitors on a day when the maximum temperature is 15 °C.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p>A data set consisting of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn></math> test scores has mean <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>.</mo><mn>5</mn></math> . One test score of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> requires a second marking and is removed from the data set.</p>
<p>Find the mean of the remaining <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math> test scores.</p>
</div>
<br><hr><br><div class="specification">
<p>In a large university the probability that a student is left handed is 0.08. A sample of 150 students is randomly selected from the university. Let <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k">
  <mi>k</mi>
</math></span> be the expected number of left-handed students in this sample.</p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the probability that exactly <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> students are left handed;</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the probability that fewer than <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="k"> <mi>k</mi> </math></span> students are left handed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A discrete random variable, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math>, has the following probability distribution:</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>k</mi><mn>2</mn></msup><mo>-</mo><mi>k</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>12</mn><mo>=</mo><mn>0</mn></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math>, giving a reason for your answer.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mo>(</mo><mi>X</mi><mo>)</mo></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A discrete random variable <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> has the following probability distribution.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>

<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find an expression for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> which gives the largest value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence, find the largest value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>E</mtext><mfenced><mi>X</mi></mfenced></math>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider the function&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f\left( x \right) = {x^2}{{\text{e}}^{3x}}">
  <mi>f</mi>
  <mrow>
    <mo>(</mo>
    <mi>x</mi>
    <mo>)</mo>
  </mrow>
  <mo>=</mo>
  <mrow>
    <msup>
      <mi>x</mi>
      <mn>2</mn>
    </msup>
  </mrow>
  <mrow>
    <msup>
      <mrow>
        <mtext>e</mtext>
      </mrow>
      <mrow>
        <mn>3</mn>
        <mi>x</mi>
      </mrow>
    </msup>
  </mrow>
</math></span>,&nbsp;&nbsp;<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x \in \mathbb{R}">
  <mi>x</mi>
  <mo>∈<!-- ∈ --></mo>
  <mrow>
    <mi mathvariant="double-struck">R</mi>
  </mrow>
</math></span>.</p>
</div>

<div class="question">
<p>The graph of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="f"> <mi>f</mi> </math></span> has a horizontal tangent line at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = 0"> <mi>x</mi> <mo>=</mo> <mn>0</mn> </math></span> and at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = a"> <mi>x</mi> <mo>=</mo> <mi>a</mi> </math></span>. Find <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="a"> <mi>a</mi> </math></span>.</p>
</div>
<br><hr><br>