An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 18

Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cats. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customer per minute.
a. What is the mean or expected number of customers that will arrive in a five 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 five-minute period.
c. Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur?