<p>The boys and girls in a school participate in an obstacle course as part of a fitness programme. The time taken by a girl to complete the obstacle course can be assumed to follow a normal distribution with mean $48$ minutes and standard deviation $7$ minutes. The time taken by a boy to complete the same obstacle course can also be assumed to follow an independent normal distribution with mean $33$ minutes and standard deviation $5$ minutes.</p>
<ol class="i-list"><li><div class="list-item-paragraph">It was noted that $80\%$ of the boys completed the obstacle course within $k$ minutes of the mean time of $33$ minutes. Find the value of $k$, correct to three significant figures.	<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Find the probability that the total time taken by two girls is more than three times that taken by a boy in completing 	the obstacle course.<span class="inline-marks">[4]</span></div></li></ol>

The boys and girls in a school participate in an obstacle course as part of a fitness programme. The time taken by a girl to complete the obstacle course can be assumed to follow a normal distribution with mean $48$ minutes and standard deviation $7$ minutes. The time taken by a boy to complete the same obstacle course can also be assumed to follow an independent normal distribution with mean $33$ minutes and standard deviation $5$ minutes.

It was noted that $80\%$ of the boys completed the obstacle course within $k$ minutes of the mean time of $33$ minutes. Find the value of $k$, correct to three significant figures.	

Find the probability that the total time taken by two girls is more than three times that taken by a boy in completing 	the obstacle course.

Normal Distribution

International Baccalaureate Higher Level Mathematics

2013 SRJC P2 Q7

2013 SRJC P2 Q7