The Exponential Distribution (Optional) · Exercise 36

Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years.

(a) Find the probability that a light bulb lasts less than one year.
(b) Find the probability that a light bulb lasts between six and 10 years.
(c) Seventy percent of all light bulbs last at least how long?
(d) A company decides to offer a warranty to give refunds to light bulbs whose lifetime is among the lowest two percent of all bulbs. To the nearest month, what should be the cutoff lifetime for the warranty to take place?
(e) If a light bulb has lasted seven years, what is the probability that it fails within the 8^th year?

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

OpenStax, Statistics · §5.3 The Exponential Distribution (Optional) · Exercise 36