Calculator of tolerance intervals for a normal distribution

Loosely speaking, a tolerance interval for a measured quantity is the interval in which there is some "likelihood" (or, of which you feel a some "level of confidence") that a specified fraction of the population's values lie, based on a sample that you measured from this population. Tolerance intervals have been widely used in statistical process control. This page will calculate tolerance intervals for any specified population fraction, and for any specified level of confidence, from the mean and standard deviation of a finite sample, under the assumption that the population is normally distributed. One-sided (upper and lower) intervals, as well as the two-sided interval, are calculated.

So:

If I measure a sample consisting of items,
and get a mean value of
and a standard deviation of
then I can be % certain
that % of the population
lies within the interval from: TBD
to: TBD (a Two-sided Tolerance Interval)
or...
lies below the value: TBD (an Upper One-sided Tolerance Interval)
or...
lies above the value: TBD (a Lower One-sided Tolerance Interval)



References:

This calculator is heavily based on this online calculator and the theory behind it is based on this online handbook, see references below.
There is also an MS Excel version of the calculator, see below.

NIST/Sematech Engineering Statistics Handbook, Section 7.2.6.3
Tolerance Intervals for Normal Distribution - online calculator
Tolerance Intervals for Normal Distribution - MS Excel


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