Fifteen percent of Australians smoke. By introducing tough laws banning brand labels on cigarette packages, Australia hopes to reduce the percentage of people smoking to 10% by 2018 (Reuters website, October 23, 2012). Answer the following questions based on a sample of 240 Australians.
a. Show the sampling distribution of p, the sample proportion of Australians who are smokers.
b. What is the probability the sample proportion will be within ± .04 of the population proportion?
c. What is the probability the sample proportion will be within ± .02 of the population proportion?