The Exponential Distribution (Optional) · Exercise 37

At a 911 call center, calls come in at an average rate of one call every two minutes. Assume that the time that elapses from one call to the next has the exponential distribution.

(a) On average, how much time occurs between five consecutive calls?
(b) Find the probability that after a call is received, it takes more than three minutes for the next call to occur.
(c) Ninety-percent of all calls occur within how many minutes of the previous call?
(d) Suppose that two minutes have elapsed since the last call. Find the probability that the next call will occur within the next minute.
(e) Find the probability that fewer than 20 calls occur within an hour.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §5.3 The Exponential Distribution (Optional) · Exercise 37