Abstract: A method of interval estimation and hypothesis test for continuous population percentiles and percentages is presented. The one-sided confidence limits and two-sided confidence intervals of percentiles and percentages may be obtained, and the tolerance limits and tolerance intervals of continuous distributions can be calculated by this method. A trustworthy test of continuous population percentiles and percentages is also presented. The interval estimating and hypothesis testing for percentiles and percentages of the three-parameter Weibull, the three-parameter logarithmic normal, the extreme value and a host of other continuous distributions most in use, which have become prominent in engineering design, are discussed at some length. The method is not only applicable to complete data but also to incomplete data and zero-failure data.

Key words: interval estimation, hypothesis test, percentile, percentage