The mean time between failures (MTBF) is a common metric used to measure the performance of manufacturing systems. MTBF is the elapsed time between failures of a system during normal operations. The failures could be caused by broken machines or computer errors, among other failures. Suppose that the MTBF for a new automated manufacturing system follows an exponential distribution with a mean of 12.8 hours. (a) What is the probability that the automated manufacturing system runs for more than 17 hours without a failure? 0.281 x (b) What is the probability that the automated manufacturing system runs for 7 or fewer hours before failure? 0.401 X (c) What is the probability that the automated manufacturing system runs for more than 6 hours but less than 11 hours before failure? 0.258 x

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