In July 2001, 45% of Americans believed the country was in a recession even though, technically, the economy had not shown two straight quarters of negative growth. For a sample of 20 Americans, make the following calculations (assume each person's belief in recession is independent of the others):
a. Compute the probability that exactly 12 people believed the country was in a recession.
b. Compute the probability that at least one person 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.