## The Normal Distribution

This is where we will use our actual data not the Z-scores.) It
follows a procedure very similar to Standard Normal Distribution.

Press ( you will see screen below)

Let's use these values from a homework assignment : The mean price of
an entree =$ 8.93 , with known
standard deviation s = $2.00

Say we want to find the probability that an entrŽe item chosen at
random will fall between $10.00 and $12.00.

Once again we want to choose "**2 : normalcdf ( **" , and press
but this time we will need to
enter 4 pieces of data. They must be entered in this order :

(**Lower limit , upper limit , mean , standard deviation**)

Here we will use the actual data not the Z-scores!

For our
problem we will use these values ( 10 , 12 , 8.93 , 2 ) You should be
looking at this screen :

Now enter **10 12 8.93 2
**

**.2339329725** will be displayed.

This is the probability that an item from the menu will fall between
$10.00 and $12.00 .

Said another way it is the area under the curve between 10.00 and
12.00 of a Normal Distribution with mean = 8.93 and known standard
deviation = 2.00.

*********************************************************
*********

If you want to see a graph of this problem we will need to return to
the distributions menu and **Arrow right** to "**DRAW**".

[We will follow the same procedure as before except we will enter 4
pieces of data.]

Press (You will see this screen
)

Now we will enter **10 12
8.93 2 **

Before you press you need to
adjust the WINDOW to fit your data !
So now press [Make sure to
adjust your window to fit your data ]

These settings will give you
the exact graph that follows (see screen below)

[For larger range between Xmin, Xmax use smaller values for
Ymax.]

Press to return to this screen:

Press (You will see this graph
with the appropriate area shaded )

This graph gives us not only the area under the curve but also shows
the lower and upper limits. By using this procedure you can find the
area under the Normal Distribution function between any two points using
your actual data.

[ Remember to adjust the WINDOW to fit your data
whenever you are graphing a problem.]

NOTE: the most common error is " ERR INVALID DIM " If you see this
error it probably indicates that a "STAT PLOT" is still "ON". You simply
need to go to STAT PLOT and turn it "OFF.".