Do you take the free samples offered in supermarkets? About 60% of all customers will take free samples. Furthermore, of those who take the free samples, about 37% will buy what they have sampled. (See reference in Problem 8.) Suppose you set up a counter in a supermarket offering free samples of a new product. The day you are offering free samples, 317 customers pass by your counter.
(a) What is the probability that more than 180 take your free sample?
(b) What is the probability that fewer than 200 take your free sample?
(c) What is the probability that a customer takes a free sample and buys the product? Use the multiplication rule for dependent events. That we are given the conditional probability P(buy | sample) = 0.37, while P(sample | = 0.60.
(d) What is the probability that between 60 and 80 customers will take the free sample and buy the product? Use the probability of success calculated in part (c).