The television show 50 Minutes has been successful for many years. That show rec

Question

The television show 50 Minutes has been successful for many years. That show recently had a share of 25, meaning that among the TV sets in use, 25% were tuned to 50 Minutes. Assume that an advertiser wants to verify that 25% 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 50 Minutes broadcast.

Find the probability that none of the households are tuned to 50 Minutes.
P(none) =

Find the probability that at least one household is tuned to 50 Minutes.
P(at least one) =

Find the probability that at most one household is tuned to 50 Minutes.
P(at most one) =

If at most one household is tuned to 50 Minutes, does it appear that the 25% share value is wrong? (Hint: Is the occurrence of at most one household tuned to 50 Minutesunusual?)

Explanation / Answer

n = 12

P = 0.25

1) P(X = 0) = 12C0 * (0.25)^0 * (0.75)^12 = 0.032

2) P(X > 1) = 1 - P(X < 1)

= 1 - P(X = 0)

= 1 - 12C0 * (0.25)^0 * (0.75)^12

= 1 - 0.032 = 0.968

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

= 12C0 * (0.25)^0 * (0.75)^12 + 12C1 * (0.25)^1 * (0.75)^11 = 0.158

D) P(at most one) =  P(X < 1) = 0.158

As the probability of the occurrence of at most one house hold tuned tuned to 50 is greater than 0.05 so it is not unusual.

As it is not unusual SO it doesn't appear that the 25% share value is wrong.

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