Continuous Uniform Distribution Question

Question

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 50.1 and 50.3 min.

Answer 1

I can give you some hints to get you started.

1.) When you're asked for a probability that a value is between x_1 and x_2 on a continuous distribution, you will want to work through the following pieces:

a.) Look up the cumulative probability function (CDF) for the distribution in question. For the continuous uniform distribution, the CDF is p(X <= x) = (x - a)/(b - a). So, in your case, a = 50, b = 52

b.) Calculate the probability of x being <= 50.3.

c.) Now, you need to account for the values of x <= 50.1

1. Calculate the probability of x being <= 50.1
2. Subtract that probability from the probability you found in step b.
3. Your answer will be what you're looking for, the probability of x being between 50.1 and 50.3

There's a book you might like called, "Statistical Distributions" by Forbes, Hastings, Evans, and Peacock. It's now in its 4th edition, but older editions can probably be purchased for very little money on alibris.com. ISBN-13: 978-0470390634

ISBN-10: 0470390638