The serum cholesterol levels of a population of 12-to 14-year-olds follow a normal distribution with mean 155 mg/dl and standard deviation 27 mg/dl (as in Example 4.1.1).
(a) What percentage of the 12- to 14-year-olds have serum cholesterol values between 145 and 165 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 145 and 165 mg/dl?
(c) If Y represents the mean cholesterol value of a random sample of nine 12- to_l4-year-olds from the population, what is Pr{145 ≤ ≤ 165}?