Question 1: The amount of time until an accident occurs at an industrial facility follows an exponential distribution with mean 40 days. a) What is the probability that the next accident occurs between 50 and 100 days? b) What is the probability that the time until an accident occurs exceeds the mean time by more than 2 standard deviations? c) Suppose it has been at least 30 days with no accidents. What is the probability that it will be at least 80 days until an accident occurs?

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