Chapter 4.5, Problem 13E

An obstetrician does ultrasound examinations on her patients between their 16th and 25th weeks of pregnancy to check the growth of each fetus. Let X equal the widest diameter of the fetal head, and let V equal the length of the femur, both measurements in mm. Assume that X and V have a bivariate normal distribution with ${\mu }_X=60.6,{\sigma }_X=11.2,{\mu }_Y=46.8,{\sigma }_Y=8.4$, and $\rho =0.94$.

(a) Find $P\left(40.5<Y<48.9\right)$.

(b) Find $P\left(40.5<Y<48.9|X=68.6\right)$.