# Problem on standard deviation

Q6  The airport branch of a car rental company maintains a fleet of 50 SUVs. The interarrival time between requests for an SUV is 2.4 hours, on average, with a standard deviation of 2.4 hours. There is no indication of a systematic arrival pattern over the course of a day. Assume that, if all SUVs are rented, customers are willing to wait until there is an SUV available. An SUV is rented, on average, for 3 days, with a standard deviation of 1 day.

a. What is the average number of SUVs parked in the company’s lot?

b. Through a marketing survey, the company has discovered that if it reduces its daily rental price of \$80 by \$25, the average demand would increase to 12 rental requests per day and the average rental duration will become 4 days. Assuming that the std. dev. values stay unchanged, should this company adopt this new pricing policy? Provide an analysis!

c. What is the average time a customer has to wait to rent an SUV? Please use the initial parameters rather than the information in (b).

d. How would the waiting time change if the company decides to limit all SUV rentals to exactly 4 days? Assume that if such a restriction is imposed, the average interarrival time will increase to 3 hours, with the standard deviation changing to 3 hours.

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