Consider the reference desk of a college library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and the service times follow an exponential probability distribution with a service rate of 12 requests per hour.
A. What is the average number in line waiting to be served?
B. What is the average time that a patron must wait to get through the system?
C. What is the utilization of the librarian?
D. What is the probability that when you arrive there will be three or more patrons ahead of you?