Many of a bank’s customers use its automated teller machine (ATM). During the early evening hours in the summer months, customer's arrive at the ATM at the rate of one every other minute (assume Poisson). Each customer spends an average of 90 seconds completing his or her transaction. Transaction times are Exponentially distributed. Assume that tire length of queue is not a constraint. Determine:
a. The average time customers spend at the machine, including waiting in line and completing transactions.
b. The probability that a customer will not have to wait upon arrival at the ATM.
c. Utilization of the ATM.
d. The probability that a customer waits four minutes or more in the line.