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 in mg/100 mL, and the data are based on the National Health Survey.

a. If 1 man aged 18–24 is randomly selected, find the probability that his serum cholesterol level is greater than 260, a value considered to be “moderately high.”

b. If 1 man aged 18–24 is randomly selected, find the probability that his serum cholesterol level is between 170 and 200.

c. If 9 men aged 18–24 are randomly selected, find the probability that their mean serum cholesterol level is between 170 and 200.

d. The Providence Health Maintenance Organization wants to establish a criterion for recommending dietary changes if cholesterol levels are in the top 3%. What is the cutoff for men aged 18–24?