Let X be a normal random variable with = 10 and = 1.5 and Y be a normal random variable with =

Let X be a normal random variable with μ = 10 and

σ = 1.5 and Y be a normal random variable with μ = 2 and

σ = 0.25. Assume X and Y are independent. Find the following probabilities.

(a) P(X<9, Y <2.5)

(b) P(X>8, Y<2.25)

(c) P(8.5 ≤ X ≤ 11.5, Y> 1.75)

(d) P(X < 13, 1.5 ≤ Y ≤ 1.8)