A consumer buys batteries for a device, each of which provides a charge lasting X EXP(2) (in days). Batteries are replaced immediately. Assume independence. a) What is the exact distribution of the lifetime provided by 15 batteries ? What is the probability that they last 30 days? b) Find the smallest number of batteries n to ensure 30 days of continuous charge with a probability of at least 0.95. This problem can be done in multiple ways.