Determination of sample sizes for setting β-content tolerance limits controlling both tails of the normal distribution

The problem of determining sample size for two-sided-β-content tolerance intervals which control both tails of the normal distribution is investigated. The tolerance limits are defined to assure that the tail proportions do not exceed specified values p₁ and p₂. We determine the minimum sample size so that, at a given confidence level, the tail proportions will not be too small, i.e., so that the tolerance interval will not be overly conservative. Tables of the sample size n and the corresponding factors are provided.