A TV show, Lindsay and Tobias, recently had a share of 20, meaning that among th

Question

A TV show, Lindsay and Tobias, recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to that show. Assume that an advertiser wants to verify that 20% share value by conducting its own survey, and a pilot survey begins with 16 households having TV sets in use at the time of a Lindsay and Tobias broadcast. a. Find the probability that none of the households are tuned to Lindsay and Tobias. (Round to three decimal places as needed.) b. Find the probability that at least one household is tuned to Lindsay and Tobias. (Round to three decimal places as needed.) c. Find the probability that at most one household is tuned to Lindsay and Tobias. (Round to three decimal places as needed.) d. If at most one household is tuned to Lindsay and Tobias, does it appear that the 20% share value is wrong? Why or why not? No, because with a 20% rate, the probability of at most one household is greater than 0.05. Yes, because with a 20% rate, the probability of at most one household is less than 0.05. Yes, because with a 20% rate, the probability of at most one household is greater than 0.05. No, because with a 20% rate, the probability of at most one household is less than 0.05.

Explanation / Answer

a. The probability is none is .80^16 = .0281

b. You can use answer from a to get this answer: the probability of at least one is 1 - <probability of none>

= 1 - .0281 = .9719

c. The probability of exactly one is 0.0281 + 0.8^16*0.2 =0.086 + 0.0056= 0.0916

Add to that the probability of none (see answer a), and you get 0.0916

d. The correct option is A

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