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# Suppose that X is a binomial random variable with n =200 ISBN: 9781118539712 55

## Solution for problem 95E Chapter 4.7

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

Step 4 of 4

##### ISBN: 9781118539712

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