An industry representative claims that 50 percent of all satellite dish owners subscribe to at least one premium movie channel. In an attempt to justify this claim, the representative will poll a randomly selected sample of dish owners.
a. Suppose that the representative's claim is true, and suppose that a sample of four dish owners is randomly selected. Assuming independence, use an appropriate formula to compute
(1) The probability that none of the dish owners in the sample subscribes to at least one premium movie channel.
(2) The probability that more than two dish owners in the sample subscribe to at least one premium movie channel.
b. Suppose that the representative's claim is true, and suppose that a sample of 20 dish owners is randomly selected. Assuming independence, what is the probability that
(1) Nine or fewer dish owners in the sample subscribe to at least one premium movie channel?
(2) More than 11 dish owners in the sample subscribe to at least one premium movie channel?
(3) Fewer than five dish owners in the sample subscribe to at least one premium movie channel?
c. Suppose that, when we survey 20 randomly selected dish owners, we fi nd that 4 of the dish owners actually subscribe to at least one premium movie channel. Using a probability you found in this exercise as the basis for your answer, do you believe the industry representative's claim? Explain.