Question: The lifespan of a car battery averages six years. Suppose the battery lifespan follows an exponential distribution.
(a) Find the probability that a randomly selected car battery will last more than four years.
(b) Find the variance and the 95th percentile of the battery lifespan.
(c) Suppose a three-year-old battery is still going strong.
(i) Find the probability the battery will last an additional five years.
(ii) How much longer is this battery expected to last?