a gallup poll showed that 30% of Americans are 5.6 Poisson Probability Distribut

Question

a gallup poll showed that 30% of Americans are 5.6 Poisson Probability Distribution 265 42/ A Gallup Poll showed that 30% of Americans are satisfied with the way things are going in the United States (Gallup website, September 12, 2012). Suppose a sample of 20 Ameri- cans is selected as part of a study of the state of the nation. a. Compute the probability that exactly 4 of the 20 Americans surveyed are satisfied with b. Compute the probability that at least 2 of the Americans surveyed are satisfied with c. For the sample of 20 Americans, compute the expected number of Americans who are d. For the sample of 20 Americans, compute the variance and standard deviation of the the way things are going in the United States. the way things are going in the United States. satisfied with the way things are going in the United States. number of Americans who are satisfied with the way things are going in the United States

Explanation / Answer

42) n = 20

P = 0.3

A) P(X = x) = nCx * Px * (1 - P)n -x

P(X = 4) = 20C4 * (0.3)^4 * (0.7)^16 = 0.13

B) P(X > 2) = 1 - P (X < 2)

= 1 - P(X = 0) + P(X = 1)

= 1 - (20C0 * (0.3)^0 * (0.7)^20 + 20C1 * (0.3)^1 * (0.7)^19)

= 1 - 0.0076 = 0.9924

C) Expected value = n * P = 20 * 0.3 = 6

D) Variance = n * P * (1 - P)

= 20 * 0.3 * 0.7 = 4.2

Standard deviation = sqrt (variance)

= sqrt (4.2) = 2.05

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