<p><strong>In this question you should state the parameters of any distribution you use.<br></strong>The times, in minutes, taken for male runners to complete a marathon follow the distribution \(\mathrm{N}(196, 24^2)\).</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Calculate the expected number of male runners who take more than \(180\) minutes to complete a marathon in a randomly chosen batch of \(80\) male runners.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">It is given that at most \(10\%\) of the fastest male runners will be eligible to join the competition. Find the qualifying time, to the nearest minute, to join the competition.<span class="inline-marks">[1]</span></div></li></ol>
<p>The times, in minutes, taken for female runners to complete a marathon follow the distribution \(\mathrm{N}(210, 30^2)\).</p>
<ol class="abc-list" start="3"><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Find the probability that the total time taken by a randomly selected male runner and \(3\) randomly selected female runners is between \(700\) and \(800\) minutes.<span class="inline-marks">[3]</span></div></li></ol>
<p>To help the group of marathon runners improve their timings for the actual competition, a sponsor provides all runners with a set of running apparel to help them reduce air drag. This reduces the timing of each male runner by \(5\%\) and reduces the timing of each female runner by \(6\%\).</p>
<ol class="abc-list" start="4"><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">Find the probability that, after being equipped with the new apparel, the total time taken by \(2\) randomly chosen female runners differs from twice the time taken by a randomly selected male runner by less than \(17\) minutes.<span class="inline-marks">[4]</span></div></li></ol>

**In this question you should state the parameters of any distribution you use.
**The times, in minutes, taken for male runners to complete a marathon follow the distribution \(\mathrm{N}(196, 24^2)\).

Calculate the expected number of male runners who take more than \(180\) minutes to complete a marathon in a randomly chosen batch of \(80\) male runners.

It is given that at most \(10\%\) of the fastest male runners will be eligible to join the competition. Find the qualifying time, to the nearest minute, to join the competition.

The times, in minutes, taken for female runners to complete a marathon follow the distribution \(\mathrm{N}(210, 30^2)\).

Find the probability that the total time taken by a randomly selected male runner and \(3\) randomly selected female runners is between \(700\) and \(800\) minutes.

To help the group of marathon runners improve their timings for the actual competition, a sponsor provides all runners with a set of running apparel to help them reduce air drag. This reduces the timing of each male runner by \(5\%\) and reduces the timing of each female runner by \(6\%\).

Find the probability that, after being equipped with the new apparel, the total time taken by \(2\) randomly chosen female runners differs from twice the time taken by a randomly selected male runner by less than \(17\) minutes.

Normal Distribution

International Baccalaureate Higher Level Mathematics

2024 ACJC P2 Q9

2024 ACJC P2 Q9