The Normal Distribution

The normal distribution, also known as the Gaussian distribution, is the most frequently used statistical distribution. The deviations of the (measured) values of many scientific, economic and engineering processes from the mean value can often be described in a good approximation by the normal distribution. Its probability density is a bell-shaped curve that runs symmetrically around the mean value (Gaussian bell curve). For some statistical analyses, the data must come from an approximately normally distributed population. The normal distribution is then used as a model
for further data analyses.

The normal distribution is completely described by the two parameters mean (μ) and standard deviation (σ). The distribution is infinite after + / - and not limited. The larger the standard deviation of a process, the more the data scatter around the mean. This makes the bell curve wider.

For any normal distribution, we find within

+ 1 standard deviation          approx. 68% of all process results

+ 2 standard deviations        approx. 95% of all process results

+ 3 standard deviations        approx. 99,73% of all process results

The percentages correspond to the proportionate area under the curve (probabilities) up to the respective numbers of
standard deviations.


The area + 3 standard deviations is called the area of natural process variation.