The Uniform Distribution · Exercise 36

The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution.

The time (in minutes) until the next bus departs a major bus depot follows a distribution with f(x) = $\frac{1}{20}$ where x goes from 25 to 45 minutes.

(a) Define the random variable. X = ________
(b) Graph the probability distribution.
(c) The distribution is ______________ (name of distribution). It is _____________ (discrete or continuous).
(d) μ = ________
(e) σ = ________
(f) Find the probability that the time is at most 30 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
(g) Find the probability that the time is between 30 and 40 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
(h) P(25 < x < 55) = _________. State this in a probability statement, similarly to parts g and h, draw the picture, and find the probability.

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

OpenStax, Introductory Business Statistics 2e · §5.2 The Uniform Distribution · Exercise 36