Chapter II

A bus runs at regular intervals between Central and Mongkok daily. The delay time, which is the difference between the actual and the scheduled arrival times at either terminus, follows a normal distribution with a mean of m minutes and a standard deviation of minutes. A negative delay time denotes an early arrival.

Records show that the bus arrives early with a probability of 0.12 and that it arrives at least 15 minutes late with a probability of 0.005. Find and show that m = 4.7.