Question

The television show 50 Minutes has been successful for many years. That show recently had a share of 16, meaning that among the TV sets in use, 16% were tuned to 50 Minutes. Assume that an advertiser wants to verify that 16% share value by conducting its own survey, and a pilot survey begins with 10 households have TV sets in use at the time of a 50 Minutes broadcast. Please show your answer to 4 decimal places.

Answer 1

0.1749

Explanation:

We are to find the probability that none of the house-holds tuned to 50 minutes.

P(tune to 50 minutes) = 0.16

p = 0.16

q = 1 - 0.16

q = 0.84

number of households (n) = 10

x = number of households that tuned at 50 minutes

since none of the household tuned, then:

x = 0

Using the binomial expression:

`P(x=x) ^nC_xp^xq^((n-x))`

`P(x=0) = ^(10)C_0 \ (0.16)^0 \ (0.84)^((10-0))`

`P(x=0) = (10!)/((10-0)!0!) \ (0.16)^0 \ (0.84)^((10))`

`P(x=0) = 1 * \ 1 * 0.1749`

P(x =0) = 0.1749