5.27An industry representative claims that50percentofall 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 sampleofdish owners.

a.Suppose that the representative's claim is true, and suppose that a sampleoffour dish

owners is randomly selected. Assuming independence, use an appropriate formula to

compute

(1)The probability that noneofthe dish owners in the sample subscribes to at leastone

premium movie channel.

(2)The probability that more than two dish owners in the sample subscribe to at leastonepremium movie channel.

b.Suppose that the representative's claim is true, and suppose that a sample of20dish

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 leastonepremium movie

channel?

c.Suppose that, when we survey20randomly selected dish owners, we find that 4ofthe

dish owners actually subscribe to at leastonepremium 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.