Cholesterol is a fatty substance that is an important part ofthe outer lining (membrane) of cells in the body of animals. Itsnormal range for an adult is 120–240 mg/dl. The Food and NutritionInstitute of the Philippines found that the total cholesterol levelfor Filipino adults has a mean of 159.2 mg/dl and 84.1% of adultshave a cholesterol level less than 200 mg/dl(http://www.fnri.dost.gov.ph/). Suppose that the total cholesterollevel is normally distributed. (a) Determine the standard deviationof this distribution. (b) What are the quartiles (the 25% and 75%percentiles) of this distribution? (c) What is the value of thecholesterol level that exceeds 90% of the population? (d) An adultis at moderate risk if cholesterol level is more than one but lessthan two standard deviations above the mean. What percentage of thepopulation is at moderate risk according to this criterion? (e) Anadult whose cholesterol level is more than two standard deviationsabove the mean is thought to be at high risk. What percentage ofthe population is at high risk? (f) An adult whose cholesterollevel is less than one standard deviations below the mean isthought to be at low risk. What percentage of the population is atlow risk?
