A tolerance interval is a statistical interval constructed to contain at least a specified proportion of a population with a specified
confidence level. If 
is the distribution function of a continuous
distribution, a two-sided 
tolerance interval ![[L,U]](/images/equations/ToleranceInterval/Inline3.svg)
is designed so that
![P[F(U)-F(L)>=p]>=1-alpha.](/images/equations/ToleranceInterval/NumberedEquation1.svg) |
The probability is over the randomness of the sample used to construct 
and 
.
A tolerance interval differs from a confidence interval, which estimates a population parameter, and from a prediction interval, which is designed to contain one or more future observations.
