Suppose that the blood cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean μ = 188 milligrams per deciliter (mg/dl) and standard deviation σ = 41 mg/dl.

a. Choose an SRS of 100 men from this population. Describe the sampling distribution of x¯.

b. Find the probability that x¯ estimates μ within ±3 mg/dl. (This is the probability that x¯ takes a value between 185 and 191 mg/dl.)

c. Choose an SRS of 1000 men from this population. Now what is the probability that x¯ falls within ±3 mg/dl of μ? In what sense is the larger sample “better”?