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class="breadcrumb"> <li><a href="../../../mathsapplications.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../1065/statistics-and-probability.html">Statistics and Probability</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">4.9 Normal Distribution</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <h2><img alt="" src="../../files/Stats/nd/ndmedium-1.jpeg" style="float: left; width: 100px; height: 100px;">Normal?</h2> <p>The normal distribution is a fascinating, naturally occurring phenomenon that has very relevant applications to understanding the world around us. When a data set is normally distributed it has some key properties that allow us to make predictions about the nature of the data set. The videos below go in to detail about those properties and how to use them to solve problems.</p> <hr> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <p><span id="docs-internal-guid-9fd720c7-7fff-4125-bb7a-ce2ed88e7d32"></span></p> <p dir="ltr"><span id="docs-internal-guid-9fd720c7-7fff-4125-bb7a-ce2ed88e7d32">In this unit you should learn to…</span></p> <ul style="list-style-type:disc;"> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation">Understand the nature and properties of data that is normally distributed</p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation"><span id="docs-internal-guid-9fd720c7-7fff-4125-bb7a-ce2ed88e7d32">Calculate probabilities using the symmetrical properties of the normal distribution</span></p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation"><span>Calculate probabilities using your GDC</span></p> </li> <li aria-level="1" dir="ltr"> <p dir="ltr" role="presentation"><span>Understand and use the inverse normal function </span></p> </li> </ul> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Slides Gallery</p> </div> </div> <div class="panel-body"> <div> <p>Use these slides to review the material and key points covered in the videos.</p> <div id="carousel-238" class="dynamic-gallery carousel slide" data-id="238"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos001.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos002.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos003.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos003.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos004.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos004.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos005.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos005.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos006.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos006.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos007.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos007.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos008.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos008.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos009.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos009.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos010.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos010.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos011.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos011.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-238/nd-no-logos012.jpeg" data-fancybox="gallery-238" title="" data-caption=""><img alt="" src="../../../std-galleries/15-238/nd-no-logos012.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-238" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-238" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos001-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos002-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos003-thumb128.jpg"><li><li data-index="3"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos004-thumb128.jpg"><li><li data-index="4"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos005-thumb128.jpg"><li><li data-index="5"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos006-thumb128.jpg"><li><li data-index="6"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos007-thumb128.jpg"><li><li data-index="7"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos008-thumb128.jpg"><li><li data-index="8"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos009-thumb128.jpg"><li><li data-index="9"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos010-thumb128.jpg"><li><li data-index="10"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos011-thumb128.jpg"><li><li data-index="11"><img title="Click to view" src="../../../std-galleries/15-238/nd-no-logos012-thumb128.jpg"><li></li></ol> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>1. What is the normal distribution?</p> </div> </div> <div class="panel-body"> <div> <p>This video intoduces the idea of data sets and distributions leading to the key properties.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/589841155"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>2. The symmetry and structure of the Normal Distribution</p> </div> </div> <div class="panel-body"> <div> <p>Here we look at the fundamental symmetrical properties and how we use them to solve problems.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/589855907"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>3.The Normal CDF function.</p> </div> </div> <div class="panel-body"> <div> <p>This video goes through using your GDC and the Normal CDF function to solve problems</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/589864141"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>4. The Inverse Normal function.</p> </div> </div> <div class="panel-body"> <div> <p>This video goes through using your GDC and the Inverse Normal function to solve problems</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/589866302"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <hr> <div class="panel panel-has-colored-body panel-violet"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div>Review these condensed 'key point' revision cards to help you check and keep ideas fresh in your mind.</div> <div> <div id="carousel-239" class="dynamic-gallery carousel slide" data-id="239"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/15-239/nd-nologos001.jpeg" data-fancybox="gallery-239" title="" data-caption=""><img alt="" src="../../../std-galleries/15-239/nd-nologos001.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-239/nd-nologos002.jpeg" data-fancybox="gallery-239" title="" data-caption=""><img alt="" src="../../../std-galleries/15-239/nd-nologos002.jpeg"></a></div><div class="item "><a class="fancy" href="../../../std-galleries/15-239/nd-nologos003.jpeg" data-fancybox="gallery-239" title="" data-caption=""><img alt="" src="../../../std-galleries/15-239/nd-nologos003.jpeg"></a></div></div><a class="left carousel-control" href="#carousel-239" role="button" data-slide="prev"><i class="fa fa-fw fa-chevron-left"></i></a><a class="right carousel-control" href="#carousel-239" role="button" data-slide="next"><i class="fa fa-fw fa-chevron-right"></i></a></div><ol class="std-carousel-indicators"><li data-index="0"><img title="Click to view" src="../../../std-galleries/15-239/nd-nologos001-thumb128.jpg"><li><li data-index="1"><img title="Click to view" src="../../../std-galleries/15-239/nd-nologos002-thumb128.jpg"><li><li data-index="2"><img title="Click to view" src="../../../std-galleries/15-239/nd-nologos003-thumb128.jpg"><li></li></ol> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-green panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test yourself</p> </div> </div> <div class="panel-body"> <div> <h4>Self checking quiz</h4> <p>Practice your understanding on these quiz questions. Check your answers when you are done and read the hints where you got stuck. If you find there are still some gaps in your understanding then go back to the videos and slides above.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="tib-quiz" data-stats="15-321-2191"><div class="label label-default q-number">1</div><div class="exercise shadow-bottom"><div class="q-question"><p>Tick the boxes next to statements you think are true. </p></div><div class="q-answer"><p>If a data set is normally distributed then we would expect it...</p><p><label class="radio"><span class="checkbox"><input class="c" type="checkbox"> To be symmetrical about the mean</span></label></p><p><label class="checkbox"><input class="c" type="checkbox"> 99% of the data to be within 3 standard deviations of the mean</label></p><p><label class="checkbox"><input type="checkbox">68% of results to be within 2 standard deviations of the mean</label></p><p><label class="checkbox"><input type="checkbox"> 95% of results to be within 1 standard deviation of the mean</label></p><p><label class="checkbox"><input class="c" type="checkbox"> 68% of results to be within 1 standard deviation of the mean</label></p></div><div class="q-explanation"></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">2</div><div class="exercise shadow-bottom"><div class="q-question"><p>The ditribution below shows a data set that is normally distributed with a mean of 50 and standard deviation of 10. For each region (labelled A - D) say the percentage of results you would expect to find.</p><p style="text-align: center;"><img alt="" src="../../files/Stats/nd/ndq3.jpg" style="width: 500px; height: 378px;"></p></div><div class="q-answer"><p>A <input type="text" style="height: auto;" data-c="2"> <span class="review"></span> %, B <input type="text" style="height: auto;" data-c="13.5"> <span class="review"></span> %, C <input type="text" style="height: auto;" data-c="68"> <span class="review"></span> %, D <input type="text" style="height: auto;" data-c="16"> <span class="review"></span> %</p></div><div class="q-explanation"><p>Based on the approximations, 68% +/-1sd, 95% +/-2sd, 99% +/-3sd and the symmetry of the diagram</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">3</div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram below shows the normal distribution curve for a data set with a mean of 30 and standard deviation of 5. What pecentage of the data set should be represented by the shaded area.</p><p style="text-align: center;"><img alt="" src="../../files/Stats/nd/ndq1.jpg" style="width: 500px; height: 354px;"></p></div><div class="q-answer"><p> <input type="text" style="height: auto;" data-c="47.5"> <span class="review"></span> %</p></div><div class="q-explanation"><p>20 is 2 standard deviations below 30. Between 20 and 40 we would expect 95% of the results. As such between 20 and 30 should be half of that.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">4</div><div class="exercise shadow-bottom"><div class="q-question"><p>The diagram below shows the normal distribution curve for a data set with a mean of 30 and standard deviation of 5. What pecentage of the data set should be represented by the shaded areas A and B?</p><p style="text-align: center;"><img alt="" src="../../files/Stats/nd/ndq2.jpg" style="width: 500px; height: 362px;"></p></div><div class="q-answer"><p>A <input type="text" style="height: auto;" data-c="2.5"> <span class="review"></span> %, B <input type="text" style="height: auto;" data-c="50"> <span class="review"></span> %</p></div><div class="q-explanation"></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">5</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider a data set that is normally distributed with a mean of 40 and standard devisation of 7. Calculate the probability that a data item selected at random will be in the categories listed below. (give answers correct to 3 sf)</p></div><div class="q-answer"><p>a) Less than 30, <input type="text" style="height: auto;" data-c="0.0766"> <span class="review"></span> </p><p>b) Greater than 45, <input type="text" style="height: auto;" data-c="0.238"> <span class="review"></span> </p><p>c) Between 42 and 46, <input type="text" style="height: auto;" data-c="0.192"> <span class="review"></span> </p></div><div class="q-explanation"><p>Enter the Normal CDF function using the Mean, Standard deviation, Lower limit and upper limit.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">6</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider a data set that is normally distributed with a mean of 4.5 and standard devisation of 0.6. Calculate the probability that a data item selected at random will be in the categories listed below. (give answers correct to 3 sf)</p></div><div class="q-answer"><p>a) Less than 3, <input type="text" style="height: auto;" data-c="0.00621"> <span class="review"></span> </p><p>b) Greater than 4.7, <input type="text" style="height: auto;" data-c="0.369"> <span class="review"></span> </p><p>c) Between 4 and 6, <input type="text" style="height: auto;" data-c="0.791"> <span class="review"></span> </p></div><div class="q-explanation"><p>Enter the Normal CDF function using the Mean, Standard deviation, Lower limit and upper limit.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">7</div><div class="exercise shadow-bottom"><div class="q-question"><p>The weights of a sample of new born babies are normally distributed with a mean of 3.1kg and a standard deviation of 0.8 kg. Find the probability that a baby selected at random from that sample weighed.</p></div><div class="q-answer"><p>a) More than 4kg, <input type="text" style="height: auto;" data-c="0.130"> <span class="review"></span> </p><p> If the sample contained 1500 babies, how many babies would you expect to be more than 4kg?</p><p> <input type="text" style="height: auto;" data-c="195"> <span class="review"></span> babies (nearest whole number)</p></div><div class="q-explanation"><p>Enter the Normal CDF function using the Mean, Standard deviation, Lower limit and upper limit. Then mutiply the probability by 1500.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">8</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider a data set that is normally distributed with a mean of 40 and standard devisation of 7. The probability of a data item selected at random being less than x, is given by 0.7.</p></div><div class="q-answer"><p>What is the value of x? <input type="text" style="height: auto;" data-c="43.7"> <span class="review"></span> (3 sf)</p></div><div class="q-explanation"><p>Use the inverse normal function with Area/Probability = 0.7, Mean = 40, sd = 7. Round correctly</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">9</div><div class="exercise shadow-bottom"><div class="q-question"><p>Consider a data set that is normally distributed with a mean of 4.5 and standard devisation of 0.6. The probability of a data item selected at random being more than x, is given by 0.45.</p></div><div class="q-answer"><p>What is the value of x? <input type="text" style="height: auto;" data-c="4.58"> <span class="review"></span> (3 sf)</p></div><div class="q-explanation"><p>Use the inverse normal function with Area/Probability = 0.55, Mean = 40, sd = 7. Probability is 0.55 because that would leave 0.45 to the right. 0.55 is the probability on the left. Round correctly</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">10</div><div class="exercise shadow-bottom"><div class="q-question"><p>The weights of a sample of new born babies are normally distributed with a mean of 3.1kg and a standard deviation of 0.8 kg. The bottom 10% of the sample were all below x kg.</p></div><div class="q-answer"><p>What is the value of x? <input type="text" style="height: auto;" data-c="2.07"> <span class="review"></span>(3 sf)</p></div><div class="q-explanation"><p>Use the inverse normal function with Area/Probability = 0.1, Mean = 3.1, sd = 0.8. Round correctly</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><p>......</p><div class="totals"><span class="score"></span><button class="btn btn-success btn-block text-center check-total"><i class="fa fa-check-square-o"></i> Check</button></div></div><hr> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam Style Questions</p> </div> </div> <div class="panel-body"> <div> <p>The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.</p> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 1</p> </div> </div> <div class="panel-body"> <div> <p style="text-align: center;"><img alt="" src="../../files/Stats/nd/nd1q.jpg" style="width: 600px; height: 360px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/589873906"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-default panel-expandable panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 2</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../files/Stats/nd/nd2.jpg" style="width: 700px; height: 256px;"></p> <p>Video solution</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/589876764"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-default panel-expandable panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Question 3</p> </div> </div> <div class="panel-body"> <div> <p style="text-align: center;"><img alt="" src="../../files/Stats/nd/nd3.jpg" style="width: 700px; height: 741px;"></p> <p>Video solution </p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/589880604"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> <p><span id="cke_bm_805E" style="display: none;"> </span></p> </div> </div> </div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="2191"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>4.9 Normal Distribution</strong> have you 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