The television show Lett3rs has been successful for many years. That show recent

Question

The television show Lett3rs has been successful for many years. That show recently had a share of 24, meaning that among the TV sets in use, 24% were tuned to Lett3rs.

Assume that an advertiser wants to verify that 24% 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 Lett3rs broadcast. Find the probability that none of the households are tuned to Lett3rs. P(none) =

Find the probability that at least one household is tuned to Lett3rs. P(at least one) =

Find the probability that at most one household is tuned to Lett3rs. P(at most one) = If at most one household is tuned to Lett3rs, does it appear that the 24% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Lett3rs unusual?) no, it is not wrong yes, it is wrong

Explanation / Answer

This is a case of binomial distribution where p=0.24 and n=13

a) P(none)=13C0*(0.24)^0*(0.76)^13 =0.0282

b) P(atleast one)=1-P(none)=1-0.0282=0.9718

c) P(atmost one) =P(none)+P(1)=13C0*(0.24)^0*(0.76)^13+13C1*(0.24)^1*(0.76)^12 =0.1441

no its not unusual

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