2) An industry representative claims that 70 percent of all satellite dish owner

Question

2) An industry representative claims that 70 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. Suppose that the representative’s claim is true, and suppose that a sample of five dish owners is randomly selected. Assume that one dish owner’s premium movie channel subscription is independent of other dish owners.
a) What is the probability that none of the dish owners in the sample subscribes to at least one premium movie channel?
b) What is the probability that more than two dish owners in the sample subscribes to at least one premium movie channel?
c) What is the probability that fewer than two dish owners in the sample subscribes to at least one premium movie channel?

3) In a shipment of 25 MP3 players 4 are bad. If you were to take a random sample of 4 MP3 players from this shipment:
a) What is the probability that none are defective?
b) What is the probability that fewer than two are defective?
c) What is the probability that exactly on is defective?

Explanation / Answer

Use binomial theorem with n=5 p=.7 a) no dish owners(1-.7)^5= 0.00243 b) 1 dish owner prob is 5* .7^1*.3^4= 0.02835 2 dish owners 5!/3!*2! .7^2*.3^3= 10 *.7^2*.3^3= 0.1323 more than 2 1-.00243-.02835-.1323= 0.83692 c) fewer than 2 .00243+.02835= 0.03078 3) Assume 4/25= .16 are bad a)None (1-.16)^4= 0.4979 b)fewer than 2; 1 is 4*.16^1* .84^3= 0.3793 So fewer than two is none plus 1 or .4979+.3793= 0.8772 c) Exactly 1 0.3793

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