# Calculation of Normal and Binomial Probabilites

Question 1: 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.

Please provide commentary and clear workings for all items.

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#### Solution Preview

Please see the attached Word document for the solution to these exercises.

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 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 ...

#### Solution Summary

In this problem we calculate the probability of an event based on a normal distribution and the probability of an event based on a binomial distribution. The solution is provided within a Word document and contains all required equations and calculations.