To understand the solution, you first need to understand that probability density functions are a representation of the probabilities of all possible outcomes in the situation being studied. Since we are looking at all possible outcomes, the total probability (represented by area on the graph) must be 100%, or 1.0 as measured in terms of a proportion.

This means that for chapters 8, 9 and many chapters beyond this that deal with continuous (measured) data, the total area under the probability density curve is 1.0. Knowing that the total are = 1.0 can help us find the height of the distribution using the simple formula for area of a rectangle:

Area of a rectangle = (base) x (height)

Substitute in the known area and the base of the rectangle to get

1.0 = (8) x (height)

Now to solve for the unknown height, divide both sides by (8)…

So Jason, what you are saying is that because area must = 1, and we know that base = 8, the f(x) therefore had to be 1/8 in order for both 8’s to cancel each other out, leaving us with 1 on each side?

But we can also do this buy using Fx=1/b-a i.e. 1/10-2=.125. Please correct me if I am wrong?

thanks

Yes you can. Your solution is the same as what I have worked out – just rearranged

Sorry, might be a little slow at this part but how did you get 1/8 as the f(x)?

Thanks in advance.

To understand the solution, you first need to understand that probability density functions are a representation of the probabilities of all possible outcomes in the situation being studied. Since we are looking at all possible outcomes, the total probability (represented by area on the graph) must be 100%, or 1.0 as measured in terms of a proportion.

This means that for chapters 8, 9 and many chapters beyond this that deal with continuous (measured) data, the total area under the probability density curve is 1.0. Knowing that the total are = 1.0 can help us find the height of the distribution using the simple formula for area of a rectangle:

= (base) x (height)Area of a rectangleSubstitute in the known area and the base of the rectangle to get

1.0 = (8) x (height)

Now to solve for the unknown height, divide both sides by (8)…

(1.0)/(8) = ((

~~8~~)x(height))/(~~8~~)1/8 = height

or…

height = 1/8

Does this help?

That clears it up, thanks!

So Jason, what you are saying is that because area must = 1, and we know that base = 8, the f(x) therefore had to be 1/8 in order for both 8’s to cancel each other out, leaving us with 1 on each side?

This is exactly right. So if instead the base had been … let’s say 3, then f(x) would need to equal 1/3.