An industry representative claims that 50% of all satellite dish owners subscribe to at least one premium movie channel. In an attempt to justify the claim, a random sample of dish owners will be selected. Assuming the claim made by the representative is true, suppose that a sample of four dish owners is selected. Write the mathematical model and determine the probability that
a. None of the dish owners in the sample subscribe subscribes to at least one premium movie channel?
b. More than two dish owners in the sample subscribe to at least one premium movie channel?
c. If a sample of 20 dish owners is randomly selected the what would be the probability that nine or fewer dish owners in the sample subscribe to at least one premium movie channel?
d. If a sample of 20 dish owners is randomly selected the what would be the probability that more than 11 dish owners in the sample subscribe to at least one premium movie channel?