A tolerance interval is a statistical interval within which, with some confidence level, a specified proportion of a population falls.
A tolerance interval can be seen as a statistical version of a probability interval. If we knew a population's exact parameters, we would be able to compute a range within which a certain proportion of the population falls. For example, if we know a population is normally distributed with mean and standard deviation, then the interval includes 95% of the population (1.96 is the z-score for 95% coverage of a normally distributed population).
However, if we have only a sample from the population, we know only the sample mean and sample standard deviation, which are only estimates of the true parameters. In that case, will not necessarily include 95% of the population, due to variance in these estimates. A tolerance interval bounds this variance by introducing a confidence level, which is the confidence with which this interval actually includes the specified proportion of the population. For a normally distributed population, a z-score can be transformed into a "k factor" for a given via lookup tables or several approximation formulas.
Read more about Tolerance Interval: Relation To Other Intervals
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