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Probability based on Normal distribution for sampling distribution.

The serum cholesterol levels in men aged 18-24 are usually distributed with a mean of 178.1 and the standard deviation of 40.7. Units are mg/100 mL, and data are based on the National Health Survey.

a. If 25 men aged 18-24 are randomly selected, find out the probability that their mean serum cholesterol level is between 165 and 200.

b. The local hospital would wants to set up a criterion for recommending dietary changes if cholesterol levels are in the top 5%. What is the cut-off serum cholesterol for men aged 18-24?

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