The lower a person’s bone mineral density (BMD), the greater the person’s risk of a bone fracture will be. BMD levels of 45-year-old African American women’s hips are approximately normally distributed with mean 1034 mg/cm2 and standard deviation 160 mg/cm2
a. A 45-year-old African American woman’s hip has BMD 986 mg/cm2. What is the z-score of the BMD level? What does it mean in this situation?
b. Another 45-year-old African American woman’s hip has BMD 666 mg/cm2. What is the z-score of the BMD level? What does it mean in this situation?
c. For negative z-scores, the risk of a hip fracture doubles for each decrease of 1 in the z-score. Compare the risks of bone fracture for the women described in parts (a) and (b).