5. The reference desk of a university 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 that service times follow an exponential probability distri- bution with a service rate of 12 requests per hour. a. What is the probability that no requests for assistance are in the system? b. What is the average number of requests that will be waiting for service? What is the average waiting time in minutes before service begins? d. What is the average time at the reference desk in minutes (waiting time plus service time)? с. What is the probability that a new arrival has to wait for service? е.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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5. The reference desk of a university 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 that service times follow an exponential probability distri-
bution with a service rate of 12 requests per hour.
What is the probability that no requests for assistance are in the system?
b. What is the average number of requests that will be waiting for service?
c. What is the average waiting time in minutes before service begins?
d. What is the average time at the reference desk in minutes (waiting time plus service
time)?
What is the probability that a new arrival has to wait for service?
е.
Transcribed Image Text:5. The reference desk of a university 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 that service times follow an exponential probability distri- bution with a service rate of 12 requests per hour. What is the probability that no requests for assistance are in the system? b. What is the average number of requests that will be waiting for service? c. What is the average waiting time in minutes before service begins? d. What is the average time at the reference desk in minutes (waiting time plus service time)? What is the probability that a new arrival has to wait for service? е.
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