The number of standard deviations required to include a given percent of a population that has a normal distribution can be looked up in a table or calculated.
To determine the number of standard deviations to include X percent of population using a table:
(1) Convert the percent to a decimal fraction.
(2) Divide the fraction by 2 (to reflect symmetry about the mean).
(3) Look up the number of standard deviations to give that value in a table.
Alternatively the values can be calculated. The following equations were fit to the normal distribution data in JMP.
number of standard deviations =
= (A * ((area)^3))) + (B * ((areas)^2))) + (C * (area)) + D
where:
• Area is the decimal fraction at the end of step 2 above.
Fraction Range |
A |
B |
C |
D |
---|---|---|---|---|
0 to 0.3643 |
0 |
2.3194752 |
2.1057859 |
0.0106404 |
0.3643 to 0.4893 |
745.29186 |
-892.7877 |
361.33164 |
-48.09123 |
0.4893 to 0.4987 |
0 |
6414.5363 |
-6266.883 |
1532.9654 |
Above 3 standard deviations the area under the normal distribution curve ranges from 0.997 to 1.000.
Area Under Normal Distribution Curve |
Number of SD |
---|---|
0.999 |
3.27 |
1.000 |
3.90 |
Purpose: To determine the number of standard deviations required to include a given percent of a population that shows a normal distribution.
Objective: other testing
ICD-10: ,