From Modern Mathematical Statistics with Applications by Devore and Berk, pg 197. Extensive experiences of fans of a certain type used in diesel engines has suggested that the exponential distribution provides a good model for time until failure. Suppose the mean time until failure is 25,000 hours. What is the probability that

a) a randomly selected fan will last at least 20,000 hours? At most 30,000 hours? Between 20,000 and 30,000 hours?

b) the lifetime of a fan exceeds the mean value by more than 2 standard deviations? More than 3 standard deviations?