Constructing a Confidence Interval for Quantiles of Normal Distribution‎, ‎one and Two Population

‎In this paper‎, ‎in order to establish a confidence interval (general and shortest) for quantiles of normal distribution in the case of one population‎, ‎we present a pivotal quantity that has non-central t distribution‎. ‎In the case of two independent normal populations‎, ‎we construct a confidence interval for the difference quantiles based on the generalized pivotal quantity and introduce a simple method for extracting its percentiles‎, ‎by which a shorter confidence interval can be constructed‎. ‎We will also examine the performance of the proposed methods by using simulations and examples‎.