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 adults 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 cholesterol below 200 mg/dl . 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% values) of this distribution?