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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
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Refer to Exercise 3.122. If it takes approximately ten

Chapter 3, Problem 125E

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QUESTION:

Problem 125E

Refer to Exercise 3.122. If it takes approximately ten minutes to serve each customer, find the mean and variance of the total service time for customers arriving during a 1-hour period. (Assume that a sufficient number of servers are available so that no customer must wait for service.) Is it likely that the total service time will exceed 2.5 hours?

Reference

Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. During a given hour, what are the probabilities that

a no more than three customers arrive?

b at least two customers arrive?

c exactly five customers arrive?

Questions & Answers

QUESTION:

Problem 125E

Refer to Exercise 3.122. If it takes approximately ten minutes to serve each customer, find the mean and variance of the total service time for customers arriving during a 1-hour period. (Assume that a sufficient number of servers are available so that no customer must wait for service.) Is it likely that the total service time will exceed 2.5 hours?

Reference

Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. During a given hour, what are the probabilities that

a no more than three customers arrive?

b at least two customers arrive?

c exactly five customers arrive?

ANSWER:

Solution:

Step 1 of 2:

It takes approximately 10 minutes to serve each customer.

Let X follows the Poisson distribution with probability density function

P(X) = 

The claim is to find the mean and variance of the total time for customers arriving during a 1 hour period and is it likely that the total service time will exceed 2.5 hours

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