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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A single librarian is stationed at a reference desk of a university library that receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 11 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 15 requests per hour. (Round your answers to four decimal places.)

(a)

What is the probability that no requests for assistance are in the system?

A single librarian is stationed at a reference desk of a university library that receives requests for assistance. Assume that a Poisson probability distribution with an arrival
rate of 11 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 15
requests per hour. (Round your answers to four decimal places.)
(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?
(c) What is the average waiting time (in hours) before service begins?
(d) What is the average time (in hours) at the reference desk (waiting time plus service time)?
(e) What is the probability that a new arrival has to wait for service?

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