Question

A Gallup poll showed that 30% of Americans are satisfied with teh way things are going in the United States. Suppose a sample of 20 Americans is selected as part of a study of the state of the nation, compute the expected number and the variance of Americans who are satisfied with the way things are going in the United States

Answer 1

Answer:

Mean of the binomial distribution  μ= 6

Variance of the binomial distribution  λ² = 4.2

Step-by-step explanation:

Explanation:-

The probability a Gallup poll showed that 30% of Americans are satisfied with the way things are going in the United States.

p = 30% = 0.3

q =1-p = 1- 0.3 =0.7

a sample of 20 Americans is selected as part of a study of the state of the nation  

size of the sample 'n' =20

we will use binomial distribution

mean:-

Mean of Americans who are satisfied with the way things are going in the United States                               (μ) = np

                                                     μ= 20 X 0.3

                                                    μ= 6

Variance:-

Variance of Americans who are satisfied with the way things are going in the United States                              λ² = n p q = 20 X(0.3)(0.7)

                                                         λ² = 4.2