[F3: 35 points] A cutting tool has a time-to-failure distribution given by a Gaussian distribution with mean and variance of 5 and 4. (a) Compute the probability of completing a 35-hr production run with eight available replacement tools [10 points] (b) Compute the probability of observing only 6 tool failures in 35 hrs of operation [10 points] (c) Estimate the probability distribution of the number of failures in a 15 hr period of operation [10 points] (d) Compute the expected (mean) number of failures in a 15 hr period of operation [5 points]