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There were 49.7 million people with some type of

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

Solution for problem 99E 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 99E

There were 49.7 million people with some type of long-lasting condition or disability living in the United States in 2000. This represented 19.3 percent of the majority of civilians aged five and over (http://factfinder.census.gov). A sample of 1000 persons is selected at random.

(a) Approximate the probability that more than 200 persons in the sample have a disability.

(b) Approximate the probability that between 180 and 300 people in the sample have a disability.

Step-by-Step Solution:

Step 1 of 4:

Here 19.3 percent of the majority of civilians aged five and over.

A sample of 100 persons is selected at random.

   

We have to find the approximate probability that more than 200 persons in the sample have a disability.We have to find the approximate probability that between 180 and 300 people in the sample have disability.

Step 2 of 4:

The probability that majority of civilians aged five and over, p= 0.193.

The total number in the sample, n=1000.

Let X be the number of civilians who aged five and over.

From the given information, it is clear that X~B(1000, 0.193)

So the mean of X,

                                     np= (10000.193).

                                         = 193

The variance of X,

                                    np(1-p)= (10000.1930.807).

                                                = 155.75

Since np>5 and n(1-p)>5, normal approximation is valid.

If X is a binomial random variable with parameters n and p,

                                                         Z=

Is approximately a standard normal variable.

Step 3 of 4

Chapter 4.7, Problem 99E 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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