A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0

Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 46.0 
and 56.0 minutes. Find the probability that a given class period runs between 50.5 and 50.75 minutes.

 

Find the probability of selecting a class that runs between 50.5 and 50.75 minutes.

Answer 1

A uniform distribution is a flat distribution that has the same probability density for every number. The area under the graph of the distribution must be 1. Since this distribution runs from 46.0 to 56.0 minutes, it has a range of 10.0 (56.0-46.0). The density must be 1/10 = 0.1, so that 10.0*0.1 = 1.0.

 

To find the probability of being between two numbers multiply the range between the numbers by the probability density.

range: 50.75-50.5 = 0.25

0.25*0.1 = 0.025

P(50.5 < x < 50.75) = 0.025