Every 6 minutes a customer arrives the vehicle inspection station and first go to registration, it takes 4 minutes on average to register the vehicle. There is only one clerk at the registration desk who works 8 hours per day. Assume inter-arrivals and service times are exponentially distributed. (Hint: You can use Exhibit 10.9 for some parts of this question.) a. What percentage of time is this clerk Idle? b. What is the average time the customer spent at the registration? c. How long is the (waiting) line, on average? d. How much time on average, does a customer spend waiting in line? e. What is the probability that an arriving customer just before entering the vehicle inspection station will find at least two other customers waiting in line? f. If the inspection station decides to hire one more clerk for the same task and with the same service time, what is the average time the customers spent at the system? Compare it with your answer b). What would be the utilization of each clerk? g. If inspection station buys a new machine which automatically recognizes and register the car, service time reduces to 3 minutes. Assume service time is constant. How does this change your answer to b)?