# [SOLVED] Finding the Area under the Curve.

• Mar 11th 2009, 06:04 PM
chasingjesus247
[SOLVED] Finding the Area under the Curve.
Please help me with this problem. I have a test in the class tomorrow. I already found the height of the distribution by using 1 divided by the total width of the distribution and got 0.5, but from there I'm stuck. Please help.

This is the problem:

A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 52.0 minutes. Find the probability that a given period runs less than 50.75 minutes.

Thank you for any help.

-Sarah (Bigsmile)
• Mar 11th 2009, 08:34 PM
matheagle
It seems that you are looking at a U(50,52) random variable.
Since the length is 52-50=2, the height of this constant density must be .5.
That's because the area must be one.
So, f(x)=.5 on 50<x<52 and zero otherwise.
You can integrate, but its just a rectangle.
The probability that X is less than 50.75 is the area under f(x) from 50 to 50.75.
That length is .75 or 3/4 and you multiply that by the height of .5 or 1/2
to give you the probability of that event, 3/8.

But why do you say that this is a normal random variable?
I would then say the mean is 51, but I have no idea what the standard deviation is.