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 14 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 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 greater than 0.05.. No. 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 less than 0.05.

Explanation / Answer

A)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    14      
p = the probability of a success =    0.2      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.043980465 [ANSWER]

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b)

Thus, P(at least one) = 1 - P(0) =   0.956019535 [ANSWER[

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c)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    14      
p = the probability of a success =    0.2      
x = the maximum number of successes =    1      
          
Then the cumulative probability is          
          
P(at most   1   ) =    0.197912093 [ANSWER]

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d)

OPTION A: NO, because with a 20% rate, the probability of at most one household is greater than 0.05. [ANSWER]

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