A certain TV show recently had a share of 90, meaning that among the TV sets in

Question

A certain TV show recently had a share of 90, meaning that among the TV sets in use, 90% were tuned to that show. Assume that an advertiser wants to verify that 90% share value by conducting its own survey, and a pilot survey begins with 9 households having TV sets in use at the time of the TV show broadcast. Complete parts (a) through (d) below. a. Find the probability that all of the households are tuned to the TV show. The probability that all of the households are tuned to the TV show is . (Round to three decimal places as needed.).

b. Find the probability that exactly8households are tuned to the TV show.

c. Find the probability that at least 8households are tuned to the TV show.

d.If at least8 households are tuned to the TV show, does it appear that the 90%share value is wrong? Why or why not?

Explanation / Answer

n = 9

p = 0.9

P(X = x) = nCx * px * (1 - p)n - x

a) P(X = 9) = 9C9 * (0.9)^9 * (0.1)^0 = 0.387

b) P(X = 8) = 9C8 * (0.9)^8 * (0.1)^1 = 0.387

c) P(X > 8) = P(X = 8) + P(X = 9) =

                 = 9C8 * (0.9)^8 * (0.1)^1 + 9C9 * (0.9)^9 * (0.1)^0 = 0.775

d) As the probability is not greater than 0.95(0.775 < 0.95), so 90% share value is not wrong.

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