About Graph.xls for graphing the
Normal Distribution
Origin: J. W. Wittwer at vertex42.com
Formulas
The general formula from advanced
mathematics is
f ( x) 
1
2 2

e
( x )2
2 2
They also give the formula for conversion from a raw score, or
data value, 𝑥, into a “standardized 𝑧 value:
z
x

The Tables Of Values
Input Values
In the left column, for graphing an entire Normal Distribution curve
There are four inputs; the cells are shaded in a bluish-green color:



The mean, 𝜇. (This is an “x” value.)
The standard deviation, 𝜎. (This is also an “x” value.)
A minimum and maximum value of 𝑧, that is, how many standard deviations to the left and to
the right of the mean should be graphed. The “real” normal distribution goes to infinity in each
direction but for practical purposes we have to pick firm limits. Anything lower than -3 or
higher than 3 is pretty unusual, and anything beyond -4 and 4 is exceedingly rare, so either of
those pairs is a good choice for the zmin and zmax values.
In the right column, for graphing regions to the left and right of selected x values
 The xmin and xmax values for a given area in the middle of the normal distribution can be
specified.
 If you want the left edge to be −∞, use the lowest x value that appears in the first table, = 𝜇 −
𝑧𝑚𝑖𝑛 ∙ 𝜎. The results will be pretty good as long as z values go at least from -3 to 3
 If you want the right edge to be ∞, use the highest x value that appears in the first table, = 𝜇 +
𝑧𝑚𝑎𝑥 ∙ 𝜎
The Tables of Values
There are several tables. Most of them have 41 data points; one has 81 data points. To our eyes, the
curves graphed from the data in these tables will appear smooth.
The first table, in rows 17-58
 z = the zmin + n/40 of the distance (zmax-zmin)
 x = converting the z value to an x value using the formula 𝑥 = 𝑧 ∙ 𝜎 + 𝜇
 f(x) = the y value that goes with the x value
o the Excel function =NORMDIST(x value, x mean, x standard deviation, FALSE)
 F(x) = the cumulative area under the curve to the left of the x value, using the
o the Excel function =NORMDIST(x value, x mean, x standard deviation, TRUE)
o Observe that it’s the fourth argument that tells Excel if you want just the function value
at that point or if you want the cumulative area to the left of that point.
The x and f(x) values are used in the first graph’s “Series1”.
The second table, rows 62-103
This seems to detail f(x) values between the xmin you’ve picked and the x value that corresponds to zmin.
It’s used in the first graph’s “Left Tail” series.
The third table, rows 105-146
This seems to detail f(x) values between the xmax you’ve picked and the x value that corresponds to zmax.
It’s used by the first graph’s “Right Tail” series.
The fourth table, rows 148-189
It is used by the second graph’s “Right Tail” series.
The fifth table, rows 192-273
The graphs
The first two graphs of Cumulative Probability
The first graph
The first graph displays the areas to the left and to the right of your xmin-to-xmax interval shaded, with
areas expressed as a percent of the total area.
The second graph
The second graph shows the area between x min and xmax shaded. The total area number is displayed
as a percent of the total area
The Cumulative Probability Graph
There’s a slider control below the graph. Drag it to change how much of the graph is shaded. There are
some hidden cells behind the graph to help make the Excel work.
Noice that there are two y-axes. Probability Density is the complicated function evaluated at that
particular z value. Cumulative probability is the total area to the left of that z-value.
The last two graphs
(Discussion and analysis not complete at this time.)