2024 RVHS H1 Q12

Roy is a personal fitness trainer who provides physical and online coaching to train one’s physical fitness. The durations, in minutes, for Roy’s physical and online coaching sessions are normally distributed with means and standard deviations as shown in the following table.

1. A physical coaching session and an online coaching session by Roy are randomly selected. Find the probability that both sessions do not last beyond \(65\) minutes each.[2]
2. Roy conducted \(10\) physical coaching sessions. Find the probability that at least \(5\) of the sessions last more than \(60\) minutes each.[3]
3. Roy conducts two physical coaching sessions and an online coaching session consecutively with a rest time of \(5\) minutes between each session. Find the probability that the total duration to conduct the \(3\) sessions is between \(190\) to \(200\) minutes.[3]

Many of Roy’s clients turn up late for their coaching sessions. Roy decides to impose a penalty of reduction of \(10\)% of the session duration if his clients turn up late.

4. On a particular day, both of Roy’s clients, one having a physical coaching session and the other having an online coaching session, turn up late. Find the probability that the difference in the durations of the two coaching sessions is within \(5\) minutes.[4]