Problem 6.7 To determine the difference, if any, between two brands of radial tires, 12 tires of each brand are tested. Assume that the lifetimes of both brands of tires come from the same normal distribution with σ = 3300.

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

(b) The engineers recorded the following values for the mean lifetimes for each brand: x = 38500, y = 41000 so x − y = −2500.

If, in fact, the lifetimes of both brands have the same distribution what is the probability that the difference between the sample means is at least as large as the observed difference 2500? That is, compute P(|X − Y | > 2500).

(c) (Part

(b) continued): Compute P(X − Y < −2500).