Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.049.0 and 59.059.0 minutes. Find the probability that a given class period runs between 50.2550.25 and 51.051.0 minutes.

Answer 1

0.075

Explanation:

Let X be the length of a class of the statistics professor. Then, the probability density function of X is given by

`f(x) = (1)/(59-49) = (1)/(10)` for x in the interval [49, 59]

because the lengths of her classes are uniformly distributed between 49 and 59 minutes.

We find the probability that a given class period runs between 50.25 and 51.0 minutes,

in the following way

`\int\limits_(50.25)^(51)f(x),dx = \int\limits_(50.25)^(51)(1)/(10),dx = (1)/(10)(51-50.25) = 0.075`