Heights of Mothers and Daughters The heights of a population of mother-daughter pairs have a bivariate normal distribution with correlation 0.5. a) Of the mothers on the 90th percentile of mothers' heights, what proportion have daughters who are taller than the 90th percentile of daughters' heights?
b) In what proportion of mother-daughter pairs are both women taller than average? (This means the mothers are taller than the average mother and the daughters are taller than the average daughter.)
[Hint: Remember that you can express standard bivariate normal variables in terms of two independent standard normal variables.]