Stat 265 - Chapter 4 Problems - Mike Kowalski 27. Suppose Z ~ Normal(0, 1) . Consider Y = Z2. a. Find the moment generating function of Y. What is the distribution of Y? b. A machine in a heavy-equipment factory produces steel rods of length X, where X is Normally distributed with a mean of 6 feet and a variance of 0.2. The cost, C, of repairing a rod that is not exactly 6 feet in length is proportional to the square of the error and is given, in dollars, by C=4(Y -6)'. If 50 rods with independent lengths are produces in a given day, find the probability that the total cost for repairs in that given day will exceed $48