A college cafeteria has a single checkout lane manned by a single cashier. Students arrive at the cash register at the rate of 2 per minute during peak lunch hour. It takes about 20 seconds to check out each student's tray. Assume that arrival rate follows a Poisson distribution and service time follows an exponential distribution. To determine the efficiency of operations, the cafeteria manager wishes to examine several queue operating characteristics. a. What is the utilization rate of this service system? b. What is the average number of students in line? c. What is the average time that each student spends in the queue? d. What is the average time that each student spends in the queue and being checked out? e. What is the probability that the cashier will be idle? f. What is the probability of five in the system