Perfluorooctanoic acid (PFOA) is a chemical used in products that coat cookware

Question

Perfluorooctanoic acid (PFOA) is a chemical used in products that coat cookware to prevent food from sticking. An agency is investigating the potential risk of PFOA as a cancer-causing agent. It is known that the blood concentration of PFOA in the general population has a mean of mu equals 6=6 parts per billion (ppb) and a standard deviation of sigma equals 10=10 ppb. An article reported on tests for PFOA exposure conducted on a sample of 323 people who live near a factory that makes one such nonstick cookware product. 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 overbarx=300 ppb. Use this information to make an inference about the true mean () PFOA concentration for the population that lives near the factory.

Explanation / Answer

mean = 6
std. dev. = 10
n = 323

(A) Considering the normal distribution, we can apply the central limit theorem to find the required probability

P(x > 7.5) = P(z > (7.5 - 6)/(10/sqrt(323)) = P(z > 2.7) = 0.0035

Hence, 0.0035 is the required probability that the average blood concentration of PFOA in the sample is greater than 7.5 ppb

(B) 300 ppb is very high compared to the population mean of 6 ppb. Hence actual probability of finding a cancer causing element is very high.

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