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

Answer:

0.075

Step-by-step explanation:

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

$f(x) = \frac{1}{59-49} = \frac{1}{10}$ 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

$\int\limits_{50.25}^{51}f(x),dx = \int\limits_{50.25}^{51}\frac{1}{10},dx = \frac{1}{10}(51-50.25) = 0.075$