Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 12 customers per hour or 0.2 customers per minute. In the same bank waiting line system, assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 18 customers per hour, or 0.3 customers per minute.


Required:

a. What is the mean or expected number of customers that will arrive in a -ve-minute period?

b. Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a -ve-minute period.

c. Delays are expected if more than three customers arrive during any -ve-minute period. What is the probability that delays will occur?