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# Normal Probabilities: Serum Cholesterol Levels in Men

You may find the probabilities using the Table or software of your choice. Please explain how you obtained your results.

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

a. If one man aged 18-24 is randomly selected, find the probability that his serum cholesterol level is greater than 220.

b. If one man aged 18-24 is randomly selected, find the probability that his serum cholesterol level is between 165 and 200.

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

d. The local hospital would wants to establish a criterion for recommending dietary changes if cholesterol levels are in the top 5%. What is the cutoff serum cholesterol for men aged 18-24?

#### Solution Summary

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculations, work, graphs and interpretations of the results are also included.

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