SRS question

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?
*please read the syllabus for correct nomenclature included in this week’s question. Some symbols don’t translate into Blackboard.

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