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Suppose that X is a binomial random variable with n =200

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

Solution for problem 95E 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 95E

Suppose that X is a binomial random variable with n =200 and p=0.4 Approximate the following probabilities:

Step-by-Step Solution:

Step 1 of 4</p>

Given that X is a binomial random variable with n=200 and p=0.4

The approximation is good for

Here np=200(0.4)=80

And nq=200(1-0.4)=120

To approximate a binomial probability with normal distribution ,a continuity correction will apply that is

             And

Now mean ()=np

                        =80

And standard deviation ()=

                                            = 

                                            =6.93

Step 2 of 4</p>

a) We have to find

Now we need to find

Now find

                    =(70.5-80)/6.93

                    = -1.37

From the standard normal tables find  =0.08534

Hence =0.08534

Step 2 of 4</p>

b) We have to find

Now =

                                   =

For 70.5, Z = -1.37

For 89.5,

                    =(89.5-80)/6.93

                    = 1.37

From the standard normal tables find   

                                                                                                 =0.91466 - 0.08534

                                                                                                 =0.82932

Hence =0.82932

Step 4 of 4</p>

c) we have to find

Now =

                       

For 79.5,

                    =(79.5-80)/6.93

                    = -0.072

For 89.5,

                    =(80.5-80)/6.93

                    = 0.072

From the standard normal tables find

                                                                                                 

                                          =0.52790 - 0.47210

                                          =0.0558

Hence =0.0558

Step 3 of 4

Chapter 4.7, Problem 95E is Solved
Step 4 of 4

Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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