2013 SRJC P2 Q7

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.

1. 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. [3]
2. 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.[4]