Standard Normal Distribution

Always start each new problem from the home screen

When calculating the probability of an event using the Normal Distribution Function there are two main categories from which you may choose on the calculator:

1. Standard Normal ( using Z-scores)

2. Normal (using the raw data).

We will first discuss the Standard Normal Distribution.

Lets say we want to find the area under the curve between z = -1 and z = 1.

This is the probability that an event is "within 1 standard deviation of the mean." We know from the Empirical Rule that this probability should be about 68%. On the calculator we need to go to the distributions menu.

First press (you should see this screen)

Highlight "2 : normalcdf( " and press (see screen below)

We need to enter only two values into the parenthesis.

They must be in this order: lower limit, ____ upper limit )

So for our problem we will enter

Remember the negative symbol is the gray button not the blue button.


.6826894809 will be displayed. This is the probability that an event will fall within 1 standard deviation of the mean value. Or stated another way it is the area under the Standard Normal curve between -1 and 1.

To see a graph of this same problem we first need to adjust the WINDOW.
So press (this screen will appear)

Make sure your settings match the above screen.

Next return to the distributions menu. Go back to this screen:

From this screen Arrow right and highlight "DRAW " . Notice that "1 : ShadeNorm( " is Highlighted. Press (see screen below)

We need to enter the same two pieces of data in the same order. So we will


Now press (see screen below)

Notice that this graph gives the area as well as the lower, and upper limits.

[You can find the area under the curve between any two Z-scores using either one of these methods just described.]

If your Z-scores fall below -4, or above 4 then you will need to adjust the X-Min, and X-Max in the WINDOW menu to fit your Z-scores.

To clear this screen press

"clrdraw" will be highlighted.

Press This will clear the drawing .