61. Extensive experience with 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?