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 Americans 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 the way things are going in the United States.

b. Compute the probability that at least 2 of the Americans surveyed are satisfied with the way things are going in the United States.

c. For the sample of 20 Americans, compute the expected number of Americans who are satisfied with the way things are going in the United States.

d. For the sample of 20 Americans, compute the variance and standard deviation of the number of Americans who are satisfied with the way things are going in the United States.