Question

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.047.0 and 57.057.0 minutes. Find the probability that a given class period runs between 51.551.5 and 51.7551.75 minutes.

Answer 1

0.025 = 2.5% probability that a given class period runs between 51.5 and 51.75 minutes.

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is between c and d is given by the following formula

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

For this problem, we have that:

`a = 47, b = 57, c = 51.5, d = 51.75`. So

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

`P(51.5 \leq X \leq 51.75) = (51.75 - 51.5)/(57 - 47) = 0.025`

0.025 = 2.5% probability that a given class period runs between 51.5 and 51.75 minutes.