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 more than 50.3 min.

P(X > 50.2) = ________.
(Report answer accurate to 2 decimal places.)

Answer 1

P(X > 50.3) = 0.85

Explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

`P(X < x) = (x - a)/(b - a)`

The probability of finding a value between c and d is:

`P(c \leq X \leq d) = (d - c)/(b - a)`

The probability of finding a value above x is:

`P(X > x) = (b - x)/(b - a)`

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min.

This means that
`a = 50, b = 52`

If one such class is randomly selected, find the probability that the class length is more than 50.3 min.

`P(X > 50.3) = (52 - 50.3)/(52 - 50) = 0.85`

So

P(X > 50.3) = 0.85