The natural tolerance of a process extends a distance of _______ on each side of the process mean.

The concept of natural tolerance in a process is fundamentally linked to the distribution of data and the principles of statistical process control. In a normally distributed process, the term "sigma" refers to the standard deviation, a measure of variability or dispersion of the process data around its mean.

The range of natural tolerance is typically defined in terms of how many standard deviations (sigmas) away from the mean the process limits extend. By convention, a process's natural tolerance is commonly considered to extend three standard deviations (or three sigma) from the mean on each side. This range encompasses approximately 99.73% of the data under the normal distribution, meaning that almost all of the process variation will fall within this interval.

Understanding this three-sigma rule is critical for defining process capability, setting performance expectations, and identifying areas for improvement. In practical terms, if a process operates within this three-sigma boundary, it is considered to be stable and capable of producing outputs within desired specifications most of the time.

The other options, while also related to standard deviations, do not accurately reflect the conventional definition of natural tolerance as it is most commonly applied in quality management and process improvement methodologies.