[Posted: Apr. 8, 2006]

Drawing a Normal Curve Using Excel


A graph representing the density function of the Normal probability distribution is also known as a Normal Curve or a Bell Curve (see Figure on right). To draw such a curve, one needs to specify two parameters, the mean and the standard deviation. The graph on the right has a mean of zero and a standard deviation of 1, i.e., (m=0, s=1). A Normal distribution with a mean of zero and a standard deviation of 1 is also known as the Standard Normal Distribution.

The goal is to create a normal distribution graph with a specified mean and standard deviation. Start by entering those values in some cells in a worksheet. The example used to illustrate the process plots a graph with a mean of 20.8 and a standard deviation of 4.8 (see Exercises 1.98 to 1.109, p. 88). Enter those values in cells E1 and F1.

Start by setting up the x-values for a standard normal curve. In A1, enter the number -4.

Select cell A1, then select Edit | Fill | Series...






Set up the resulting dialog box as on the right. Using a step value of 0.25 is typically adequate. However, if you want more data points, use a smaller number, such as 0.1.

Next, in cell B1, enter the formula =A1*4.8+20.8. This converts the standard normal distribution to the distribution of interest. In C1, enter the formula =NORMDIST(B1,20.8,4.8,0). This provides y-values for the distribution of interest. Propagate B1:C1 down to cover all the rows that contain data in column A.

Plot columns B and C in a XY Scatter chart (smoothed lines without markers):

















The result should be as given below:

-4 1.6 2.78813E-05 20.8 4.8
-3.75 2.8 7.34574E-05
-3.5 4 0.000181809
-3.25 5.2 0.000422718
-3 6.4 0.000923302
-2.75 7.6 0.001894492
-2.5 8.8 0.003651729
-2.25 10 0.006612427
-2 11.2 0.011248118
-1.75 12.4 0.017974441
-1.5 13.6 0.026982832
-1.25 14.8 0.038051893
-1 16 0.050410568
-0.75 17.2 0.062736965
-0.5 18.4 0.073346943
-0.25 19.6 0.080555858
0 20.8 0.083112975
0.25 22 0.080555858
0.5 23.2 0.073346943
0.75 24.4 0.062736965
1 25.6 0.050410568
1.25 26.8 0.038051893
1.5 28 0.026982832
1.75 29.2 0.017974441
2 30.4 0.011248118
2.25 31.6 0.006612427
2.5 32.8 0.003651729
2.75 34 0.001894492
3 35.2 0.000923302
3.25 36.4 0.000422718
3.5 37.6 0.000181809
3.75 38.8 7.34574E-05
4 40 2.78813E-05