The Exponential Distribution · Exercise 27

Suppose that the length of phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to eight minutes.

(a) Define the random variable. X = ________________.
(b) Is X continuous or discrete?
(c) X ~ ________
(d) μ = ________
(e) σ = ________
(f) Draw a graph of the probability distribution. Label the axes.
(g) Find the probability that a phone call lasts less than nine minutes.
(h) Find the probability that a phone call lasts more than nine minutes.
(i) Find the probability that a phone call lasts between seven and nine minutes.
(j) If 25 phone calls are made one after another, on average, what would you expect the total to be? Why?

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

OpenStax, Introductory Statistics 2e · §5.3 The Exponential Distribution · Exercise 27