The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 8 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 9 requests per hour. 1. What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places. 2. What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 8 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 9 requests per hour.

1. What is the probability that a new arrival has to wait for service? If required, round your answer to four decimal places.

2. What is the average number of requests that will be waiting for service? If required, round your answer to four decimal places.

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