Chapter 4.5, Problem 10E

In a college health fitness program, let X denote the weight in kilograms of a male freshman at the beginning of the program and Y denote his weight change during a semester. Assume that X and Y have a bivariate normal distribution with ${\mu }_X=72.30,{\sigma }_X^2=110.25,{\mu }_Y=2.80,{\sigma }_Y^2=2.89,$ and $\rho =-0.57$.

(The lighter students tend to gain weight. while the heavier students tend to lose weight.) Find

(a) $P\left(2.80\le Y\le 5.35\right)$.

(b) $P\left(2.76\le y\le 5.34|X=82.3\right)$.