8.77 If Y has a distribution, then Y can be represented as where has a distribution and the ’s are independent. It is not surprising, then, that Y will be approximately normally distributed for large n. Use this fact in the solution of the following problem.

A machine in a heavy-equipment factory products steel rods of length Y, where Y is a normally distributed random variable with a mean of 6 inches and a variance of 0.2. The cost C (in dollars) of repairing a rod that is not exactly 6 inches in length is given by where . If 50 rods with independent lengths are produced in a given day, approximate the probability that the total cost for repairs exceeds $48.