8. The lifetime T of an alkaline battery is exponentially distributed, and AVERAGE LFFETIME of T is 15 hours. (a) What are the MEAN and STANDARD DEVIATION of the battery's lifetime? Show process. (3 points) (b) What are the probabilities for the battery to last between 13 and 16 hours, (3 points) (c) What is the probability P(T35 hours T20 hours)? Show process. (3 points).