The Uniform Distribution · Exercise 34

For each probability and percentile problem, draw the picture.

A subway train arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution.

(a) Define the random variable. X = _______
(b) X ~ _______
(c) Graph the probability distribution.
(d) f(x) = _______
(e) μ = _______
(f) σ = _______
(g) Find the probability that the commuter waits less than one minute.
(h) Find the probability that the commuter waits between three and four minutes.
(i) Sixty percent of commuters wait more than how long for the train? State this in a probability question, similarly to parts g and h, draw the picture, and find the probability.

OpenStax, Introductory Statistics 2e · §5.2 The Uniform Distribution · Exercise 34