A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 53.0 minutes. Find the probability that a given class period runs between 51.5 and 51.75 minutes. Find the probability of selecting a class that runs between 51.5 and 51.75 minutes.

Step-by-step answer:

Given:

class time uniformly distributed between 48 and 53 minutes (range 5 minutes)

Find probability that the class period runs between 51.5 and 51.75 minutes.

Solution:

Uniformly distributed means that the probability that the class time is the same for any minute (out of 5), i. e. 20%, or probability density is 0.2 / minutes, no matter which minute.

The interval between 51.5 and 51.75 is 0.25 minutes, so the probability of class period within that range is 0.25 minutes * 0.2 / minute = 0.05.