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

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