Question $6[3$ marks$]$: An airline organization has one reservation clerk on duty in its local branch at any given time. The clerk handles information regarding passenger reservations and flight timings. Assume that the number of customers arriving during any given period is Poisson distributed with an arrival rate of eight per hour and that the reservation clerk services customers in six minutes on average, with an exponentially distributed service time.

$($a$)$ What is the probability that a customer has to wait?

$($b$)$ What is the average time a customer spends in the system?