What is the formula for calculating BMD when the Z score is known?

The formula for calculating Bone Mineral Density (BMD) when the Z score is known involves the relationship between the observed BMD, the average or expected BMD for a reference population, and the standard deviation of the population.

In this context, the Z score represents the number of standard deviations a given individual's BMD is from the expected mean value of a healthy reference group. Therefore, to find the actual BMD from the Z score, you adjust the expected BMD by adding the product of the Z score and the standard deviation. This allows you to account for how far the Z score indicates the individual's BMD deviates from the expected value.

Thus, the formula is correctly expressed as BMD = expected BMD + (z-score x SD). This calculation effectively translates the standard deviation-based measure of deviation (the Z score) back into the actual BMD units that clinicians use for diagnosis and treatment planning.

The other formulas present variations that do not correctly apply the standard statistical relationship involving the Z score and how it modifies the expected BMD to yield an actual BMD measurement.