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 μX = 72.30, σ2x = 110.25, μY = 2.80, σ2y = 2.89, and ρ = −0.57. (The lighter students tend to gain weight, while the heavier students tend to lose weight.) Find
(a) P(2.80 ≤ Y ≤ 5.35).
(b) P(2.76 ≤ y ≤ 5.34 | X = 82.3).