Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 45.0 and 55.0 minutes.
A) Find the probability that a given class period runs between 51.5 and 51.75 minutes.
B) Find the probability of selecting a class that runs between 51.5 and 51.75 minutes.
(Round to three decimal places as needed.)

Answer 1

Answer:

0.025

Step-by-step explanation:

Hello!

Given that the classes are uniformly distributed between 45.0 and 55.0 minutes, the propability distribution will be:

$P(x)=\frac{1}{55-45} = \frac{1}{10}$

Now, we are looking for a probability P(51.5<x<51.75) which can be computed as:

$P(51.5<x<51.75) = \int\limits^{51.75}_{51.5} {P(x)} \, dx =\frac{1}{10}\int\limits^{51.75}_{51.5} {} \ dx\\\\P(51.5<x<51.75) = \frac{51.75-51.5}{10}=\frac{0.25}{10}$

Therefore:

P(51.5<x<51.75) = 0.025

or

P(51.5<x<51.75) = 2.5%

I strongly believe that the answer for both questions have the same answer, I believe this because there is no additional info for a given class  or selecting a class. I think both probabilities are the same.