Government data show that 9 of the American population are a

Government data show that 9% of the American population are at least 75 years of age. To test a random-digit dialing device, you use the device to call randomly chosen residential telephones in your county. Of the 250 members of the households contacted, 4% are 75 years or older.

B. What is the probability that a random sample of 250 respondents would contain less than 4% of individuals at least 75 years of age? (Use 3 decimal places)

Solution

Population proportion = 9%

Sample proportion = 4%

sample size = 250

Mean of sample proportion =4%

variance = (0.04)(0.96)/250

Std dev = 0.0124

P(proportion <4%)

z score for 4% =   =- 1.612

Prob (Z<-1.612) = 0.5-0.4463 = 0.0537

=0.054