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Question

The television show September Road has been successful for many years. That show recently had a share of 17, meaning that among the TV sets in use, 17% were tuned to September Road. Assume that an advertiser wants to verify that 17% share value by conducting its own survey. A pilot survey begins with 14 households that have TV sets in use at the time of a September Road broadcast.

a) Find the probability that none of the households are tuned to September Road.

P(none) = 

b) Find the probability that at least one household is tuned to September Road.

P(at least one) =    

c) Find the probability that at most one household is tuned to September Road.

P(at most one) =  

d) If at most one household is tuned to September Road, does it appear that the 17% share value is wrong? (Hint: Is the occurrence of at most one household tuned to September Road unusual?)  Use a value of 5% or lower for "unusual".

Answer 1

Binomial probability

p=0.17, N=14

Prob(x=0)=

(14 choose 0) (0.17)^0 (0.83)^14 = 0.07363

Prob(x=1) = (14 choose 1)(0.17)(0.83)^13 = 0.2111505....

Prob( at least one) = 1 - prob(zero) = 1 - 0.07363 = 0.92637

Prob( at most one) = prob(x=0) + prob(x=1) = 0.284...

You can do a hypothesis test for population proportion