question archive The television show Ghost Whistler has been successful for many years
The television show Ghost Whistler has been successful for many years
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The television show Ghost Whistler has been successful for many years. That show recently had a share of 28, meaning that among the TV sets in use, 28% were tuned to Ghost Whistler. Assume that an advertiser wants to verify that 28% share value by conducting its own survey, and a pilot survey begins with 13 households have TV sets in use at the time of a Ghost Whistler broadcast.
Find the probability that none of the households are tuned to Ghost Whistler.
P(none) = 
Find the probability that at least one household is tuned to Ghost Whistler.
P(at least one) =
Find the probability that at most one household is tuned to Ghost Whistler.
P(at most one) =
If at most one household is tuned to Ghost Whistler, does it appear that the 28% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Ghost Whistler unusual?)
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Answer :
Probability that a house is tuned to ghost whistler = 0.28
P(none) = (1-0.28)^13 = 0.0139740
P(atleast one ) = 1 - 0.0139740 = 0.986025
P(almost one) = p(none) + p(one) = 0.0139740 + 13C1(0.28)^1(1-0.28)^12 = 0.084620
No. It doesn't mean that 28% share is wrong because there may be the chance that sample drawn may consist only of the houses that are not tuned to ghost whistlers. It's a sampling issue.
