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# Calculate the finite population corrections(a) For

ISBN: 9781118539712 55

## Solution for problem 152E Chapter 3.8

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 152E

Calculate the finite population corrections

(a) For Exercises 3-141 and 3-142, for which exercise should the binomial approximation to the distribution of X be better?

(b) For Exercise 3-141, calculate P(X = 1) and P(X = 4), assuming that X has a binomial distribution, and compare these results to results derived from the hypergeometric distribution.

(c) For Exercise 3-142, calculate P(X = 1) and P(X = 4), assuming that X has a binomial distribution, and compare these results to the results derived from the hypergeometric distribution.

(d) Use the binomial approximation to the hypergeometric distribution to approximate the probabilities in Exercise 3-146. What is the finite population correction in this exercise?

Step-by-Step Solution:

Step 1 of 4</p>

a) Given that in the exercise (3-141)  N=100, n=4 and K=20

In the exercise (3-142)  N=20, n=4 and K=4

The binomial approximation is best for the sample when the population size is larger

The population size is large in exercise (3-141)

Hence the binomial approximation is best for (3-141)

Step 2 of 4</p>

b) We have to find P(X=1) and P(X=4) assuming X has a binomial distribution for

exercise (3-141)

From the given exercise N=100, n=4, K=20

Here the probability (p)=K/N

=20/100

=0.2

And q=1-0.2=0.8

The pmf of binomial distribution is

Now

=0.4096

And

=0.0016

For the exercise (3-141) by using hypergeometric distribution

And

Step 3 of 4

Step 4 of 4

##### ISBN: 9781118539712

This full solution covers the following key subjects: distribution, exercise, binomial, results, Hypergeometric. This expansive textbook survival guide covers 97 chapters, and 2005 solutions. The full step-by-step solution to problem: 152E from chapter: 3.8 was answered by , our top Statistics solution expert on 07/28/17, 07:57AM. The answer to “Calculate the finite population corrections(a) For Exercises 3-141 and 3-142, for which exercise should the binomial approximation to the distribution of X be better?(b) For Exercise 3-141, calculate P(X = 1) and P(X = 4), assuming that X has a binomial distribution, and compare these results to results derived from the hypergeometric distribution.(c) For Exercise 3-142, calculate P(X = 1) and P(X = 4), assuming that X has a binomial distribution, and compare these results to the results derived from the hypergeometric distribution.(d) Use the binomial approximation to the hypergeometric distribution to approximate the probabilities in Exercise 3-146. What is the finite population correction in this exercise?” is broken down into a number of easy to follow steps, and 107 words. Since the solution to 152E from 3.8 chapter was answered, more than 239 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers , edition: 6. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9781118539712.

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