Chapter 4.5, Problem 5E

Let X denote the height in centimeters and Y the weight in kilograms of male college students. Assume that X and Y have a bivariate normal distribution with parameters ${\mu }_X=185,{\sigma }_X^2=100,{\mu }_Y=84,{\sigma }_Y^2=64$, and $\rho =\frac{3}{8}$.

(a) Determine the conditional distribution of Y, given that $X=190$

(b) Find $P\left(86.4<Y<95.36|X=190\right)$.