2026 RI P2 Q7

In this question, you should state the parameters of any distributions you use.

In a running competition, the time taken by members from the Sports Recreational Club to complete a \(20\) km race is normally distributed with a mean of \(105\) minutes and a standard deviation of \(12\) minutes.

1. Find the probability that a randomly chosen Sports Recreational Club member finishes the \(20\) km race in less than \(100\) minutes.[1]
2. Find the time that is exceeded by \(10\%\) of the Sports Recreational Club members.[1]

Members from the Swift Runners Club completed the same \(20\) km race. After analysing their results, it was found that \(36\%\) of them completed the race in less than \(95\) minutes and \(8\%\) of them completed the race in more than \(125\) minutes. You may assume the Swift Runners Club members’ running times can be modelled using a normal distribution with mean \(\mu\) and standard deviation \(\sigma\).

3. Determine the values of \(\mu\) and \(\sigma\).[4]
4. Using the values of the parameters found in part (c), find the probability that the total running time of \(2\) randomly chosen Swift Runners Club members is less than \(1.8\) times of the running time of a randomly chosen Sports Recreational Club member.
   State an assumption you have made in your calculation.[4]