<p style="margin-bottom: 1.25rem">A school has a large number of girls. For each year-group it may be assumed that the heights of girls are normally distributed, with average heights and standard deviations as given in the following table.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 450px;"><colgroup><col style="width: 150px;"><col style="width: 150px;"><col style="width: 150px;"></colgroup><thead><tr style="height: 23px;"><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>Year-group</p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>Average height</p><p style="text-align: center;"></p></th><th style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>Standard deviation</p></th></tr></thead><tbody><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$11$-year old girls</p><p style="text-align: left;"></p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p style="text-align: center;">$1.1$ m</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$0.2$ m</p></td></tr><tr style="height: 23px;"><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$16$-year old girls</p><p style="text-align: left;"></p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p style="text-align: center;">$1.7$ m</p></td><td style="height: 23px; min-height: 23px; text-align: center; --cell-justify: center"><p>$0.3$ m</p></td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-paragraph">For each of the following cases, state, with a reason, whether or not a normal model is likely to be appropriate.</div><ol class="i-list"><li><div class="list-item-paragraph">The number of days since her last birthday of a randomly chosen $11$-year old girl from the school.</div></li><li><div class="list-item-paragraph">The height of a pupil chosen at random from the combined group of $11$-year old and $16$-year old girls in the school.<br></div></li><li><div class="list-item-paragraph">The average height of a randomly chosen sample of eight $11$-year old girls from the school</div></li></ol></li><li><div class="list-item-paragraph">Find the probability such that</div><ol class="i-list"><li><div class="list-item-paragraph">each of the two randomly chosen $11$-year old girls is taller than $1.2$ m.</div></li><li><div class="list-item-paragraph">the total height of two randomly chosen $11$-year old girls is more than $2.4$ m.</div></li></ol></li></ol>
<p>Explain why the answer to <strong>(b)(ii)</strong> is higher than that of <strong>(b)(i)</strong>.</p>

A school has a large number of girls. For each year-group it may be assumed that the heights of girls are normally distributed, with average heights and standard deviations as given in the following table.

<p>Average height</p><p style="text-align: center;"></p>

<p>$11$-year old girls</p><p style="text-align: left;"></p>

<p>$16$-year old girls</p><p style="text-align: left;"></p>

For each of the following cases, state, with a reason, whether or not a normal model is likely to be appropriate.

Linear Combinations, Parameter Estimation, and Real-World Modeling

Linear Combinations, Parameter Estimation, and Real-World Modeling