Problem 1

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 24 customers per hour or 0.4 customer per minute.

Question

In the Willow Brook National Bank waiting line system (see Problem 1), assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute.

Use the exponential probability distribution to answer the following questions:

a. What is the probability the service time is one minute or less?
b. What is the probability the service time is two minutes or less?
c. What is the probability the service time is more than two minutes?