The problems of interval estimating the quantiles of normal distributions in one- and two-sample cases are considered. For the one-sample case, we show that the classical confidence interval (CI) based on the noncentral t (NCT) distribution and the CI (Chakraborti and Li 2007) based on the uniformly minimum variance unbiased estimator of the population quantile are the same. We also propose simple closed-form alternative CI for a quantile on the basis of a normal approximation to the NCT distribution. Furthermore, we develop fiducial distributions for population quantiles using the NCT distribution as well as the approximate normal distribution. These fiducial distributions are used to find fiducial and approximate closed-form CIs for a ratio/difference of normal quantiles. The properties of the CIs are evaluated and compared using Monte Carlo simulation. Three examples are given to illustrate the methods of finding confidence intervals for quantiles and ratio/difference of quantiles.
