1. Let X and Y be independent chi-square random variables with 14 and 5 degrees of freedom, respectively. Find
(a) P (|X - Y | ≤ 11.15),
(b) P (|X - Y | ≥ 3.8).
2. A particular type of vacuum-packed coffee packet contains an average of 16 ounces. It has been observed that the number of ounces of coffee in these packets is normally distributed with σ = 1.41 ounce. A random sample of 15 of these coffee packets is selected, and the observations are used to calculate s. Find the numbers a and b such that P (a ≤ S2 ≤ b) = 0.90.