Question

A TV​ show, Lindsay and Tobias​, recently had a share of 10​, meaning that among the TV sets in​ use, 10​% were tuned to that show. Assume that an advertiser wants to verify that 10​% share value by conducting its own​ survey, and a pilot survey begins with 10 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. nothing ​(Round to three decimal places as​ needed.) b. Find the probability that at least one household is tuned to Lindsay and Tobias. nothing ​(Round to three decimal places as​ needed.) c. Find the probability that at most one household is tuned to Lindsay and Tobias. nothing ​(Round to three decimal places as​ needed.) d. If at most one household is tuned to Lindsay and Tobias​, does it appear that the 10​% share value is​ wrong? Why or why​ not? A. ​Yes, because with a 10​% ​rate, the probability of at most one household is greater than 0.05. B. ​No, because with a 10​% ​rate, the probability of at most one household is less than 0.05. C. Yes​, because with a 10​% ​rate, the probability of at most one household is less than 0.05. D. No​, because with a 10​% ​rate, the probability of at most one household is greater than 0.05.

Answer 1

n = 10

p = 0.1

It is a binomial distribution.

P(X = x) = nCx * p^x * (1 - p)^{n - x}

a) P(X = 0) = 10C0 * (0.1)^0 * (0.9)^10 = 0.3487

b) P(X > 1) = 1 - P(X < 1)

                  = 1 - P(X = 0)

                  = 1 - 0.3487 = 0.6513

c) P(X < 1) = P(X = 0) + P(X = 1)

                 = 10C0 * (0.1)^0 * (0.9)^10 + 10C1 * (0.1)^1 * (0.9)^9

                = 0.7361

d) Option - D) No, because with 10% rate, the probability of at most one household is greater than 0.05.