Problem:
The new-accounts office at the Savings and Loans Bank enrolls all new customers in checking accounts. During the three-week period in September encompassing the beginning of the new school year at State University, the bank opens a lot of new accounts for students. The bank estimates that the arrival rate during the period will be Poisson distributed with an average of four customers per hour. The service time is exponentially distributed with an average of 12 minutes per customer to set up a new account.
The bank wants to determine the operating characteristics for this system to determine if the current person is sufficient to handle the increased traffic.
a. Probability of no customers in the system
b. Average number of customers in the system
c. Average number of customers waiting
d. Average time in the system
e. Average time waiting
f. Probability that the new-accounts office will be busy and that the customer must wait. Explain the solution in detail.