MathCastle
Statistics & DataSuperchallengeTwo Variables

Two Variables · Superchallenge problem

Fathers' heights and adult sons' heights are both normally distributed with the same mean and the same standard deviation, and their correlation is r=0.5r = 0.5. A father is at the 9090th percentile of fathers' heights. At what percentile of sons' heights is the least-squares prediction of his son's height? Round to the nearest whole percentile.