According to a recent poll, 27% of adults in a certain area have high levels of cholesterol. they report that such elevated levels "could be financially devastating to the regions healthcare system" and are a major concern to health insurance providers. according to recent studies, cholesterol levels in healthy adults from the area average about 210 mg/dl, with a standard deviation of about 20 mg/dl, and are roughly normally distributed. assume that the standard deviation of the recent studies is accurate enough to be used as the population standard deviation. if the cholesterol levels of a sample of 45 healthy adults from the region is taken, answer parts a through d.

(a) what shape will the sampling distribution of the mean have?
(b) what is the mean of the sampling distribution?
(c) what is the standard deviation?
(d) if the sampling size were increased to 100, how would your answers to parts (a) - (c) change?