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 51.5 and 51.7 min. P(51.5 < X < 51.7)

Answer 1

0.1 = 10% probability that the class length is between 51.5 and 51.7 min, that is, P(51.5 < X < 51.7) = 0.1.

Explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distributon has two bounds, a and b, and the probability of finding a value between c and d is given by:

`P(c \leq X \leq d) = (d - c)/(b - a)`

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min.

This means that
`a = 50, b = 52`

If one such class is randomly selected, find the probability that the class length is between 51.5 and 51.7 min.

`P(51.5 \leq X \leq 51.7) = (51.7 - 51.5)/(52 - 50) = (0.2)/(2) = 0.1`

0.1 = 10% probability that the class length is between 51.5 and 51.7 min, that is, P(51.5 < X < 51.7) = 0.1.