Individuals with low bone density (osteoporosis) have a high risk of broken bones (fractures). Physicians who are concerned about low bone density in patients can refer them for specialized testing. Currently, the most common method for testing bone density is dual energy X-ray absorptiometry (DEXA). The bone density results for a patient who undergoes a DEXA test usually are reported in grams per square centimeter (g/cm²) and in standardized units.

Judy, who is 25 years old, has her bone density measured using DEXA. Her results indicate bone density in the hip of 948 g/cm² and a standardized score of z = −1.45. The mean bone density in the hip is 956 g/cm² in the reference population of 25-year-old women like Judy.3

a. Judy has not taken a statistics class in a few years. Explain to her in simple language what the standardized score reveals about her bone density.

b. Use the information provided to calculate the standard deviation of bone density in the reference population.