33. Fifty percent of Americans believed the country was in a recession, even though technically the economy had not shown two straight quarters of negative growth (BusinessWeek, July 30, 2001). For a sample of 20 Americans, make the following calculations.

a. Compute the probability that exactly 12 people believed the country was in a recession.

b. Compute the probability that no more than five people believed the country was in a recession.

c. How many people would you expect to say the country was in a recession?

d. Compute the variance and standard deviation of the number of people who believed the country was in a recession.