Suppose that in a certain large population mothers' heights X and daughters' heights

Y are both normally distributed with mean 65 inches and standard deviation 3 inches. Suppose

further that mothers' and daughters' heights are jointly normal (i.e., they are bivariate normal

variables) with correlation 1/2.

(a) Among all daughters whose mothers were approximately 68 inches tall, what fraction are taller

than their mothers?

(b) What fraction of all mother/daughter pairs have average height above 66 inches?

(c) What is the average height of all mothers with above-average heights, that is, what is

E(X | X > 65)?