A tolerance interval covers at least a proportion P of the population with confidence γ, computed by the normal K-factor method and a distribution-free order-statistic method side by side.
A confidence interval brackets a parameter (the mean); a tolerance interval brackets the population itself: 'with 95% confidence, at least 95% of all units fall between L and U'. That's the question spec-setting, acceptance, and reference-limit work actually ask. The normal method computes x̄ ± k·s where the K-factor accounts jointly for the uncertainty in x̄ and s (via the noncentral t / χ² distributions).
The nonparametric method uses extreme order statistics: the coverage of (x₍₁₎, x₍ₙ₎) follows a Beta distribution, so the achieved confidence depends only on n — no distribution assumed, but much larger samples are needed for the same tightness.
One numeric column + coverage P + confidence γ + one- or two-sided.
Normal (K-factor) and nonparametric bounds, with a Shapiro-Wilk normality check advising which to trust.
Wider than the naive x̄ ± 2s because it guarantees coverage with confidence. If normality is rejected, use the nonparametric bounds (or transform first).