Suppose that X and Y are independent random variables, where X is normally distributed with mean 45 and standard deviation 0.5 and Y is normally distributed with mean 20 and standard deviation 0.1. Evaluate a double integral numerically to find the given probability correct to three decimal places.

(a) P(40 ≤ X ≤ 50, 20 ≤ Y ≤ 25)

(b) P(4(X – 45)² + 100(Y – 20)² ≤ 2)