Continuous Probability Distributions

[jbraun]

The April rainfall in Flagstaff, AZ follows a uniform distribution between 0.5 and 3.00 inches.
What is the probability of less than 1 inch of rain for the month?

a = 0.5 b = 3.00 mean = 1.75 inches and standard deviation = 0.722 (rounded)

I have the answer in the back of the book, but I don't understand how they came up with the formula:

P(x<1) = 1/3.0-0.5 times 1-0.5/1

I think I need to use the uniform distribution formula (P(x) = 1/(b-a) if a</= x</=b and 0 elsewhere) but I don't understand where the multiplication piece is coming from. In this case, x is more than a and less than b.

 

[tkhunny]

How is your Plane Geometry?

Draw a horizontal axis. Make sure 0.5 and 3.0 will fit on it and place vertical line segments in those two locations.

Draw a horizontal line segment, above and parallel to your axis, perpendicular to and connecting the two vertical lines at 0.5 and 3.0.

You should see a rectangle. The width of this rectangle is 3.0 - 0.5 = 2.5.

Using the property that the total of all the probability must be unity (1), calculate the height of the rectangle.

You should now be able to answer the question with visual clarity. Start by drawing a vertical line segment at 1.0.

Let's see what you get.