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The serum cholesterol levels of a population of 12- to 14-year-olds follow a normal distribution with mean 162 mg/dl and standard deviation 28 mg/dl.
(a) What percentage of the 12- to 14-year-olds have serum cholesterol values between 152 and 172 mg/dl?
(b) Suppose we were to choose at random from the population a large number of groups of nine 12- to 14-year-olds each. In what percentage of the groups would the group mean
cholesterol value be between 152 and 172 mg/dl?
(c) If Y represents the mean cholesterol value of a random sample of nine 12- to 14-year-olds from the population, what is Pr(152 ≤ Y≤ 172)?
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