A TV show, Lindsay and Tobias, recently had a share of 30, meaning that among th

Question

A TV show, Lindsay and Tobias, recently had a share of 30, meaning that among the TV sets in use, 30% were tuned to that show. Assume that an advertiser wants to verify that 30% share value by conducting its own survey, and a pilot survey begins with 13 households having TV sets in use at the time of a Lindsay and Tobias broadcast. Find the probability that none of the households are tuned to Lindsay and Tobias. (Round to three decimal places as needed.) Find the probability that at least one household is tuned to Lindsay and Tobias. (Round to three decimal places as needed.) Find the probability that at most one household is tuned to Lindsay and Tobias. (Round to three decimal places as needed.) If at most one household is tuned to Lindsay and Tobias, does it appear that the 30% share value is wrong? Why or why not? No, because with a 30% rate, the probability of at most one household is less than 0.05. Yes, because with a 30% rate, the probability of at most one household is greater than 0.05. No, because with a 30% rate, the probability of at most one household is greater than 0.05. Yes, because with a 30% rate, the probability of at most one household is less than 0.05.

Explanation / Answer

Solution:-

p = 30/100 = 0.30

n = 13

a) The probability that none of the households are turned to Lindsay and Tobais is 0.0097.

x = 0

By applying binomial distribution:-

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

P(x = 0) = 0.0097

b) The probability that atleast one households are turned to Lindsay and Tobais is 0.9903

x = 1

By applying binomial distribution:-

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

P(x > 1) = 0.9903

c) The probability that atmost one households are turned to Lindsay and Tobais is 0.06367.

By applying binomial distribution:-

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

P(x < 1) = 0.06367

d) No, Because with 30% rate, the probability of atmost one household is greater than 0.05.

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