An article titled "You're Eating That?", published in the New York Times, discussed consumer perception of food safety. The article cited research by the Food Marketing Institute, which indicates that 66% of consumers in the United States are confident that the food they buy is safe. Suppose that six consumers in the United States are randomly sampled and asked whether they are confident that the food they buy is safe.
Determine the probability that the number answering in the affirmative is
a. Exactly two.
b. Exactly four.
c. At least two.
d. Determine the probability distribution of the number of U.S. consumers in a sample of six who are confident that the food they buy is safe.
e. Strictly speaking, why is the probability distribution that you obtained in part (d) only approximately correct?
f. What is the exact distribution called?