37% of Americans are satisfied with the way things are going in the U.S. Suppose

Question

37% of Americans are satisfied with the way things are going in the U.S. Suppose a sample of 60 Americans is selected as a part of the study.

A.) What is the probability that exactly 17 of 60 Americans are satisfied witht he way things are going?

B.) What is the probability that no more than 12 of the 60 American are satisfied with the way things are going?

C.) What is the expected number of Americans in the sample who are satisfied?

D. What is the standard deviation of the number of Americans who are NOT satsfied with the way things are going?

Explanation / Answer

P(satisfied with the way things are going) = 0.37

n =60

expected number of Americans in the sample who are satisfied = np = 60*0.37 = 22.2

variance of number of Americans in the sample who are satisfied = np(1-p) = 60*0.37*(1-0.37) = 13.986

standard deviation = 3.74

A) probability that exactly 17 of 60 Americans are satisfied witht he way things are going = 60C17*(0.37)17(0.63)43 = 0.0416

B)Using normal approximation

z value of 12 is (12-22.2)/3.74 = -2.727 ,p value =0.003196

probability that no more than 12 of the 60 American are satisfied with the way things are going =0.0032

C)expected number of Americans in the sample who are satisfied = np = 60*0.37 = 22.2

D)standard deviation of the number of Americans who are NOT satsfied with the way things are going = standard deviation of the number of Americans who are satsfied with the way things are going = 3.74

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