The Environmental Protection Agency EPA sets standards for e

The Environmental Protection Agency (EPA) sets standards for environmental emissions from hazardous substances. The EPS suggested that radon gas levels exceeding 4 picocurues per liter (pc/l) are associated with increased risk of lung cancer. A real estate developer owns 60 buildings in Phoenix and measurements indicate that 3 of the buildings have radon levels in excess of 4 pc/l.

A.) Give an estimate of , the proportion of buildings in the city having radon levels that exceed the EPA guidlines. In other words, find p-hat.

B.) If in fact = 0.04, is it reasonable to assume that the sampling distribution of p-hat, the sample proportion, is approximately normal? If not, what is the smallest sample size required so that the sampling distribution of p-hat is approxamately normal? Please explain.

Solution

a) p-hat = 3/ 60 = 0.05

b)

standard deviation: (0.05*0.95) / 60 = 7.91x10^-4