Problem 5 (12 points): The temperature at which a heating system automatically shuts off is normally distributed with mean 68 and standard deviation 1. The heating system is tested 5 times and the temperatures at which it shuts off are recorded. Let X be the sample mean and S the sample variance of the 5 recorded temperatures. Find the following probabilities: (a) P{X < 67.5} (b) P{0.85 S2 1.15} (c) P({X < 67.5} {0.85 S 1.15})