The Uniform Distribution · Exercise 39

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) X ~ ________
(c) Graph the probability distribution.
(d) The distribution is ______________ (name of distribution). It is _____________ (discrete or continuous).
(e) μ = ________
(f) σ = ________
(g) 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.
(h) 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.
(i) P(25 < x < 55) = _________. State this in a probability statement, similarly to parts g and h, draw the picture, and find the probability.
(j) Find the 90^th percentile. This means that 90% of the time, the time is less than _____ minutes.
(k) Find the 75^th percentile. In a complete sentence, state what this means. (See part j.)
(l) Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 30 minutes.

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

OpenStax, Introductory Statistics 2e · §5.2 The Uniform Distribution · Exercise 39