The Exponential Distribution · Exercise 30

The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about five years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement.

(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 the person retired after age 70.
(h) Do more people retire before age 65 or after age 65?
(i) In a room of 1,000 people over age 80, how many do you expect will NOT have retired yet?

This is an open-ended exercise: its source gives no single answer.

OpenStax, Introductory Statistics 2e · §5.3 The Exponential Distribution · Exercise 30