Calculating Acceptable Ranges

Many physical and biological processes are well-modeled by a distribution having a roughly bell-like shape. This curve is called the gaussian, bell curve, or normal distribution. The normal distribution has the following characteristics:

- 68.3% of the area lies between the mean minus one standard deviation (1 SD) and x¯ plus 1 SD
- 95.5% of the area lies between x¯ - 2 SD and x¯ + 2 SD
- 99.7% of the area lies between x¯ - 3 SD and x¯ + 3 SD

For example, if a certain control gives a mean test result of 5.6 with an SD of 0.8, then 95.5% of future control test values will be in the range of 4.0 - 7.2, which is 2 standard deviations of the mean. Values that fall outside of these limits may not be acceptable, depending on the laboratory's QC rules, and could indicate a problem with the measuring system.