## This is an approximate table of probabilities which relates
dispersion units above or below the mean value to the total
amount of the sample that is contained * outside * that region
for values less than zero and * inside * the region for values greater
than zero.

-3.0 .001
-2.5 .006
-2.2 .014
-2.0 .023
-1.8 .035
-1.6 .055
-1.4 .081
-1.2 .115
-1.0 .158
-0.8 .212
-0.6 .274
-0.4 .345
-0.2 .421
0.0 .500
+0.2 .579
+0.4 .655
+0.6 .725
+0.8 .788
+1.0 .841
+1.2 .885
+1.4 .919
+1.6 .945
+1.8 .964
+2.0 .977
+2.2 .986
+2.5 .994
+3.0 .999
The use of this table is not complicated. Here is how it works.

Example 1:

You determine that some event lies +0.4 above the mean.
What is the probability that an event that large could happen.

- 65.5% of the sample is contained within that value. That means
100 -65.5 or 34.5% is outside of that range.
- The probability of an event at least that large happening is then
34.5% of approximately 1 out of 3.

Example 2

You determine that some event lies -1.6 below the mean.
What is the probability that an event this small could happen?

- If you are below the mean, the calculation is a bit easier.
-1.6 encloses 5.5% of the distribution. In other words
100 -5.5% = 94.5% of the time, the data values will be higher than
-1.6 below the mean.
- The probability of an event at least this small is therefore
5.5% or about 1 out of 20.