The Uniform Distribution · Exercise 33

For each probability and percentile problem, draw the picture.

According to a study by Dr. John McDougall of his live-in weight loss program, the people who follow his program lose between six and 15 pounds a month until they approach trim body weight. Let’s suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month.

(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 individual lost more than 10 pounds in a month.
(h) Suppose it is known that the individual lost more than 10 pounds in a month. Find the probability that he lost less than 12 pounds in the month.
(i) P(7 < x < 13|x > 9) = __________. State this result in a probability question, 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, Statistics · §5.2 The Uniform Distribution · Exercise 33