On an inequality for the normal distribution arising in bioequivalence studies

For (mu, sigma(2)) not equal (0, 1), and 0 < z < infinity, we prove that [GRAPHICS] where phi and Phi are, respectively, the p.d.f. and the c.d.f. of a standar d normal random variable. This inequality is sharp in the sense that the ri ght-hand side cannot be replaced by a larger quantity which depends only on mu and sigma. In other words, for any given (mu, sigma) not equal (0, 1), the infimum, over 0 < z < infinity, of the left-hand side of the inequality is equal to the right-hand side. We also point out how this inequality ari ses in the context of defining individual bioequivalence.