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Answer: Suppose that X has a Poisson distribution with a

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 97E Chapter 4.7

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 97E

Suppose that X has a Poisson distribution with a mean of 64. Approximate the following probabilities:

Step-by-Step Solution:

Step 1 of 3:

Let X has a poisson distribution with a mean of 64.

We have to find the following probabilities.

P(X>72)P(X<64)P(60<X68)

Step 2 of 3:

Here X~Poisson(=64).

                                           Mean, =64.

                                          Variance, =64.

Let Z follows approximate normal distribution and variable, Z= .

                                       

                                                    P(X>72)= P(Z> )    [ by adding the correction factor 0.5]

                                                                   = P(Z>1.06)

                                                                   = 1- P(Z<1.06)

From the standard normal table, P(Z<1)= 0.8554.

                             

                                                     P(X>72)= 1- 0.8554

                                                                   = 0.1446

Therefore, the probability P(X>72) is 0.1446.

(b)

                                          P(X<64)= P(Z<)  [ by subtracting the correction factor 0.5]

                                                                  = P(Z<)

                                                                  = P(Z<-0.062)

                                                           

From the standard normal table, P(Z<0.062)= 0.4761.

Therefore, the probability P(Z<64)= 0.4761

Step 3 of 3

Chapter 4.7, Problem 97E is Solved
Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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