Let X be a normal random variable with = 15.0 and = 3 and Y be a normal random variable with =

Let X be a normal random variable with μ = 15.0 and σ = 3 and Y be a normal random variable with μ = 20 and σ = 1. Assume X and Y are independent. Find the following probabilities.

(a) P(X<12, Y <19)

(b) P(X> 16, Y <18)

(c) P(14≤ X < 16, Y > 22)

(d) P(11≤ X ≤ 20, 17.5 ≤ Y≤ 21)