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 Caucasian women’s hips are approximately normally distributed with mean 920 mg/cm2 and standard deviation 136 mg/cm2.
a. A 45-year-old Caucasian woman’s hip has a BMD of 893 mg/cm2. What is the z-score of the BMD level? What does it mean in this situation?
b. Another 45-year-old Caucasian woman’s hip has a BMD of 485 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).