The Uniform Distribution · Exercise 31

For each probability and percentile problem, draw the picture.

According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, 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) Graph the probability distribution.
(c) f(x) = _________
(d) μ = _________
(e) σ = _________
(f) Find the probability that the individual lost more than ten pounds in a month.
(g) Suppose it is known that the individual lost more than ten pounds in a month. Find the probability that he lost less than 12 pounds in the month.
(h) P(7 < x < 13 $|$ x > 9) = __________. State this 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, Introductory Business Statistics 2e · §5.2 The Uniform Distribution · Exercise 31