Suppose that in a certain population, individual Solution The problem involves changing the unit of measurement of the reference variable. For example, let X denote height in inches and let Y denote height in feet. Since 1 foot is equal to 12 inches, Y = X=12 or X = 12Y . Since 1 inch is equal to 2:54 centimeters, height measure in centimeters (Z) satis(cid:12)es Z = 2:54X. All these transformations are scale transformations, a particular instance of the general linear transformation. This implies (recall that the normal family is closed under all linear transformations) that the transformed variable is again normally distributed, with di(cid:11)erent parameters. 1. Since 6 feet correspond to 12(cid:1)6 = 72 inches, the problem is to derive P(X > 72). Using reduction to the standard normal distribution XST: ===================================================================== ===================== P(X > 72) = 1 FX(72) = 1 FXST ((72 70)=3) = 1 FXST (2=3) \' 0:2514: ===================================================================== ====================== A better approximation is provided by R function p norm. > 1 - pnorm(12 * 6, mean = 70, sd = 3) [1] 0.2524925.