A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 45.045.0 and 55.055.0 minutes. Find the probability that a given class period runs between 50.550.5 and 51.2551.25 minutes.

Step-by-step explanation:

For this case we define X as our random variable representing the lenghts of her classes in minutes.

We know that the distribution for X is uniform and is given by:

The density function is given by:

for other case

The cumulative distirbution function is given by:

And we want to find this probability:

We can find this probability using the cumulative distribution function and we got:

you could deduce the conclusion directly using the facts pertaining to the specific situation.

hope this .