Continuous uniform distribution

Question

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is less than 51.7 min.

P(X < 51.7) = Incorrect 

(Report answer accurate to 2 decimal places.)

Answer 1

Because it is a continuous uniform distribution, we can view it as how much area of the rectangle is shaded problem

First, draw a rectangle.

Mark the bottom left corner as 50mins, and the bottom right corner as 52mins.

The height of the rectangle is irrelevant, but lets say it is 0.5. (because total probability = 1)

The total are of the rectangle is width x height = 2 x 0.5 = 1

Now, mark 51.7 on the x axis, and draw a vertical line to divide the rectangle into two. Because the question is asking you for less than 51.7 mins. We can shade in the left side of the rectangle.

if the width of the rectangle is only from 50 mins to 51.7 mins (1.7), the new area will become 1.7 x 0.5 = 0.85

We can simply do 0.85/1 to get the percentage of the shaded area of the entire rectangle.

0.85/1 = 0.85

Now we have 0.85 as the answer.