Question

The television show September Road 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 September Road. Assume that an advertiser wants to verify that 28% share value by conducting its own survey, and a pilot survey begins with 12 households have TV sets in use at the time of a September Road broadcast.

Find the probability that none of the households are tuned to September Road.
P(none) = ___?

Find the probability that at least one household is tuned to September Road.
P(at least one) = ____?

Find the probability that at most one household is tuned to September Road.
P(at most one) = ____?

If at most one household is tuned to September Road, does it appear that the 28% share value is wrong? (Hint: Is the occurrence of at most one household tuned to September Road unusual?)

___ yes, it is wrong

___ no, it is not wrong

Answer 1

a) The probability that none of the households are tuned to September Road is computed as:

= (1 - p)ⁿ = ( 1 - 0.28)¹² = 0.0194

Therefore 0.0194 is the required probability here.

b) Now the probability that at least one household is tuned to September Road is computed here as:

= 1 - Probability that none of the households are tuned to September Road

= 1 - 0.0194

= 0.9806

Therefore 0.9806 is the required probability here.

c) Now the probability that at most one household is tuned to September Road is computed here as:

P(X = 0) + P(X = 1)

= 0.72¹² + 12*0.72¹¹*0.28

= 0.1010

Therefore 0.1010 is the required probability here.

d) Given that at most one household is tuned to September Road, the event is not unusual, because the probability here is 0.1010 > 0.05.

Therefore No , it is not wrong would be the correct answer here.