In a study of 1744 women in their thirties, the women’s HDL cholesterol levels are approximately normally distributed with mean 54 mg/dl and standard deviation 15.0 mg/dl. In a study of 955 women in their fifties, the women’s HDL cholesterol levels are approximately normally distributed with mean 57 mg/dl and standard deviation 17.2 mg/dl
a. Suppose one of the women in their thirties has an HDL reading of 60 mg/dl. Find the z-score of the reading relative to the women in their thirties. What does it mean in this situation?
b. Suppose one of the women in their fifties has an HDL reading of 62 mg/dl. Find the z-score of the reading relative to the women in their fifties. What does it mean in this situation?
c. HDL is the “good” cholesterol. The higher a person’s HDL level, the lower the person’s risk of heart attack and stroke will be. Doctors sometimes judge a characteristic of a per- son’s health by comparing it to others of the same age. Limiting such a comparison to just those in the study, determine which of the two women described in parts (a) and (b) has the relatively better HDL reading.
d. How is it possible that of the two women described in parts (a) and (b), the woman who has the higher HDL reading has the lower z-score?