Larger sample Suppose that the blood cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean m = 188 milligrams per deciliter

(mg/dl) and standard deviation s = 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 m within

±3 mg/dl. (This is the probability that x– takes a value between 185 and 191 mg/dl.) Show your work.

(c) Choose an SRS of 1000 men from this population.

Now what is the probability that x– falls within

±3 mg/dl of m? Show your work. In what sense is the larger sample “better”?