Problem 6.6 Let X denote the sample mean of a random sample of size n1 = 16 taken from a normal distribution N(, 36) and

Problem 6.6 Let X denote the sample mean of a random sample of size n1 = 16 taken from a normal distribution N(µ, 36) and let Y denote the sample mean of a random sample of size n2 = 25 taken from a different normal distribution N(µ, 9). Assume X and Y are independent.

(a) Describe the distribution of X − Y . Name it and identify the parameters.

(b) Compute P(X − Y > 5).

(c) Compute P(|X − Y | > 5).