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 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