Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 57.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.

Answer 1

0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.

Explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

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

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

Uniformly distributed between 47.0 and 57.0 minutes.

This means that
`a = 47, b = 57`

Find the probability that a given class period runs between 51.25 and 51.5 minutes.

`P(c \leq X \leq d) = (51.5 - 51.25)/(57 - 47) = 0.025`

0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.