Cholesterol is a fatty substance that is an important part of the outer lining (membrane) of cells in the body of animals. Its normal range for an adult is 120–240 mg/dl. The Food and Nutrition Institute of the Philippines found that the total cholesterol level for Filipino adults has a mean of 159.2 mg/dl and 84.1% of adults have a cholesterol level less than 200 mg/dl (http://www.fnri.dost.gov.ph/). Suppose that the total cholesterol level is normally distributed.

(a) Determine the standard deviation of this distribution.

(b) What are the quartiles (the 25% and 75% percentiles) of this distribution?

(c) What is the value of the cholesterol level that exceeds 90% of the population?

(d) An adult is at moderate risk if cholesterol level is more than one but less than two standard deviations above the mean. What percentage of the population is at moderate risk according to this criterion?

(e) An adult whose cholesterol level is more than two standard deviations above the mean is thought to be at high risk. What percentage of the population is at high risk?

(f) An adult whose cholesterol level is less than one standard deviations below the mean is thought to be at low risk. What percentage of the population is at low risk?