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

1.Choose an SRS of 100 men from this population. What is the sampling distribution of x? What is the probability that x takes a value between 185 and 191 mg/dl? This is the probability that x estimates u within ± 3 mg/dl.
2.Choose an SRS of 1000 men from this population. Now what is the probability that x falls within ± 3 mg/dl of u? The larger sample is much more likely to give an accurate estimate of u.
3.Compute the z score and find the level of probability on the normal probability table. Why are the probability levels so different?