11 The Judy Gray Income Tax Service is analyzing its customer service operations during the month prior to the April filing deadline. On the basis of past data it has been estimated that cus- tomers arrive according to a Poisson process with an average interarrival time of 12 minutes. The time to complete a retum for a customer is exponentially distributed with a mean of 10 min- utes. Based on this information, answer the following questions:

a. If you went to Judy, how much time would you allow for getting your return done?

b. On average, how much room should be allowed for the waiting area?

c. If Judy stayed in the office 12 hours per day, how many hours on average, per day, would she be busy?

d. What is the probability that the system is idle?

e. If the arrival rate remained unchanged but the average time in system must be 45 minutes or less, what would need to be changed?