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

Answer:

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

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

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

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

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.

$P(c \leq X \leq d) = \frac{51.5 - 51.25}{57 - 47} = 0.025$

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