In a certain geographical region, the height X of women has a normal distribution with E(X) = 168 cm and Var(X) = 64 cm, whereas the height Y of men has a normal distribution with E(Y) = 175 cm and...

In a certain geographical region, the height X of women has a normal distribution with E(X) = 168 cm and Var(X) = 64 cm, whereas the height Y of men has a normal distribution with E(Y) = 175 cm and Var(Y) = 100 cm.

Determine the probability that a randomly selected woman is taller than a randomly selected man.

Hint The desired probability has structure P(X ≥ Y) = P(X + (−Y) ≥ 0).