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Refer to Exercise 3.122. Assume that arrivals occur

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 126E Chapter 3

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 126E

Problem 126E

Refer to Exercise 3.122. Assume that arrivals occur according to a Poisson process with an average of seven per hour. What is the probability that exactly two customers arrive in the two-hour period of time between

a 2:00 P.M. and 4:00 P.M. (one continuous two-hour period)?

b 1:00 P.M. and 2:00 P.M. or between 3:00 P.M. and 4:00 P.M. (two separate one-hour periods that total two 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?

Step-by-Step Solution:

Solution:

Step 1 of 2:

 For a departmental store arrival of the customers is 7 per hour.

  1. The claim is to find the probability that exactly two customers arrive in the two-hour period of  time, 2:00 P.M and 4:00 P.M.  ( one continuous two-hour period)

The mean of the distribution is  = 7 per hour and 14 per two hours

Let X follows the Poisson distribution with probability density function

P(X) =

P( x = 2) =

               = 0.0000815

Hence, the probability that exactly two customers arrive in the two-hour period of  time, 2:00 P.M and 4:00 P.M.  ( one continuous two-hour period) is 0.0000815


Step 1 of 2:

b)

The claim is to find the probability that exactly two customers arrive in the two-hour period of  time, 1:00 P.M and 2:00 P.M or between 3:00 P.M and 4:00 P.M ( two separate one-hour periods that total two hours.

P( x = 2) =

               = 0.0000815

Hence, The claim is to find the probability that exactly two customers arrive in the two-hour period of  time, 1:00 P.M and 2:00 P.M or between 3:00 P.M and 4:00 P.M ( two separate one-hour periods that total two hours is 0.0000815


Step 2 of 1

Chapter 3, Problem 126E is Solved
Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

Since the solution to 126E from 3 chapter was answered, more than 875 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 126E from chapter: 3 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. The answer to “Refer to Exercise 3.122. Assume that arrivals occur according to a Poisson process with an average of seven per hour. What is the probability that exactly two customers arrive in the two-hour period of time betweena 2:00 P.M. and 4:00 P.M. (one continuous two-hour period)?b 1:00 P.M. and 2:00 P.M. or between 3:00 P.M. and 4:00 P.M. (two separate one-hour periods that total two hours)?ReferenceCustomers 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 thata no more than three customers arrive?b at least two customers arrive?c exactly five customers arrive?” is broken down into a number of easy to follow steps, and 110 words. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. This full solution covers the following key subjects: customers, arrive, period, Poisson, average. This expansive textbook survival guide covers 32 chapters, and 3350 solutions.

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Refer to Exercise 3.122. Assume that arrivals occur