Perfluorooctanoic acid (PFOA) is a chemical used in Teflon-coated cookware to prevent food from sticking. The EPA is investigating the potential risk of PFOA as a cancer-causing agent (Science News Online, August 27, 2005). It is known that the blood concentration of PFOA in people in the general population has a mean of µ = 6 parts per billion (ppb) and a standard deviation of σ = 10 ppb. Science News Online reported on tests for PFOA exposure conducted on a sample of 326 people who live near DuPont's Teflon-making Washington (West Virginia) Works facility.
a. What is the probability that the average blood concentration of PFOA in the sample is greater than 7.5 ppb?
b. The actual study resulted in  = 300 ppb. Use this information to make an inference about the true mean µ PFOA concentration for the population of people who live near DuPont's Teflon facility.