Calls to the service center at AutoMax occur at a rate of 27 per hour and follow a Poisson distribution. A single operator answers the calls and can handle an average 25 calls per hour with service times following an exponential distribution. If a call arrives while the operator of AutoMax’s phone system is busy with another customer, up to 2 callers may be placed in a queue to await service. If a call arrives when the queue is full the caller receives a busy signal.

a. What is the probability that a caller waits in the queue?

b. How many minutes can customers expect to wait in the queue?

c. What is the probability that a caller receives a busy signal?

d. What should be the maximum queue length if AutoMax wants there to be no more than approximately a 0.2 probability that calling customers receive a busy signal?