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 20,000 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?
c. What is the life expectancy of the median fan life?