The lifetime of an Acme heat pump has an Exponential distribution with a mean of 12 years. Suppose that a random Acme heat pump is selected. a. Find the probability that the pump's lifetime is more than 20 years. b. Find the probability that the pump's lifetime is less than 11 years. c. Find the probability that the pump's lifetime is between 10 and 22 years. Find the 95% percentile of the heat pump's lifetime. d. e. Find the probability that the pump lasts more than 20 years given it lasts longer than 15 years.

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