Passengers arriving at a suburban rail ticket office during the morning peak commuter period frequently have to wait for service. There is one clerk who issues tickets and provides an information service for passengers. The manager has received complaints regarding the time passengers spend in the queue waiting to be served, and she wishes to investigate possible methods of reducing the queueing time. Possible ideas include employing a second ticket clerk who could either share the work of the existing clerk or perhaps handle enquiries only. Another idea may be to collect fares on the train. The manager decided to collect data on arrivals and service times over a number of days, and her figures are summarized Required a) Compute the midpoints for arrival and service times and apply it to construct the appropriate random number mappings for the random variables starting from 00 . (3 marks) b) Simulate 15 customers arriving at the using the random numbers given below. (12 marks) c) What is the average time a customer waits for service? (1 mark) d) What is the average time a customer is in the system (wait plus service time) (2 marks) e) What is the percent of time the clerk is busy with customers? (2 marks) Hint (midpoint for 60 to under 90=(60+90)/2=75 sec)