Discuss the below:
Q: A railway company operates a number of different services. One of these connects two cities and the journey time is assumed to be normally distributed with a mean of 125 minutes and a standard deviation of 5 minutes.
The company operates a scheme where it refunds 25% of the fare paid if the journey takes longer than 131 minutes.
i) Show that the probability that a refund will be paid on a particular journey is 0.1151.
ii) The company operates 12 services a day. Calculate the probability that a refund will be paid on exactly two journeys during a particular day assuming that the journey time of each service is independent of the others
iii) Explain why the assumption in part ii) may not hold true.