<p>The heights, in metres, of female and male students in a school follow normal distributions with the following data.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr style="height: 40px;"><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">Mean Height (metres)</th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">Variance Height (metres${^2}$)</th></tr></thead><tbody><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">Female</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">$1.6$</td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center">$0.04$</td></tr><tr style="height: 43px;"><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">Male</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$1.75$</td><td style="height: 43px; min-height: 43px; text-align: center; --cell-justify: center">$0.05$</td></tr></tbody></table></div></div>
<p>Find the probability that</p>
<ol class="i-list"><li><div class="list-item-paragraph">Two randomly selected male are taller than twice a randomly selected female.</div></li><li><div class="list-item-paragraph">A randomly selected male student is taller than a randomly selected female student by at least $20$ cm.</div></li><li><div class="list-item-paragraph">The difference in height between a randomly selected male and a female is more than $30$ cm.</div></li><li><div class="list-item-paragraph">The heights of two randomly selected female students both exceed $1.5$ m.</div></li><li><div class="list-item-paragraph">The total height of two randomly selected female students is more than $3$ m.</div></li></ol>
<p>Comment on the difference in answers for part <strong>(iv)</strong> and <strong>(v)</strong>.</p>

The heights, in metres, of female and male students in a school follow normal distributions with the following data.

Two randomly selected male are taller than twice a randomly selected female.

A randomly selected male student is taller than a randomly selected female student by at least $20$ cm.

The difference in height between a randomly selected male and a female is more than $30$ cm.

The heights of two randomly selected female students both exceed $1.5$ m.

The total height of two randomly selected female students is more than $3$ m.

Comment on the difference in answers for part **(iv)** and **(v)**.

Normal Distribution

H2 Math

International Baccalaureate Higher Level Mathematics

Probability Problems Involving Normal Distributions of Student Heights

Probability Problems Involving Normal Distributions of Student Heights

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