RI Normal Distribution Tutorial Q10

Every weekday, the last train from Bedok Station leaves the station at 11.29 pm. Its travel time \(X\) (in minutes) from Bedok Station to Redbridge Station may be taken to follow a normal distribution with mean \(30\) and variance \(9\).

1. Find the travel time exceeded by \(90\%\) of the trips made by the last train.[2]

At 11.40 pm every weekday, Abel walks from his workplace to Redbridge Station to catch the last train. The time \(Y\) (in minutes) he takes follows a normal distribution with mean \(16\) and variance \(4\).

2. Find the probability that the train arrives at Redbridge Station after 12 am and Abel arrives before 12 am[2]
3. Find the probability that Abel will not miss the train.[3]
4. Explain why the answer to part (iii) is greater than the answer to part (ii).[1]

The time \(W\) (in minutes) taken by Dina to walk from her workplace to Redbridge Station has a mean of \(4\) and a variance of \(6\).

Explain why \(W\) is unlikely to be normally distributed.[1]