Refer to Exercise 5.2.4. Suppose we take a random sample of sixteen 12- to 14-year-olds from the population.
(a) What is the probability that the mean cholesterol value for the group will be between 145 and 165?
(b) What is the probability that the mean cholesterol value for the group will be between 140 and 170?
Exercise 5.2.4
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?
(e) 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}?