‎In several statistical problems‎, ‎non-parametric confidence intervals for population quantiles can be constructed and their coverage probabilities can be computed exactly‎, ‎but cannot in general be rendered equal to a pre-determined level‎. ‎The same difficulty arises for coverage probabilities of non-parametric prediction intervals for future observations‎. ‎One solution to this difficulty is to interpolate between intervals which have the closest coverage probability from above and below to the pre-determined level‎. ‎In this paper‎, ‎confidence intervals for population quantiles are constructed based on interpolated upper and lower records‎. ‎Subsequently‎, ‎prediction intervals are obtained for future upper records based on interpolated upper records‎. ‎Additionally‎, ‎we derive upper bounds for the coverage error of these confidence and prediction intervals‎. ‎Finally‎, ‎our results are applied to some real data sets‎. Also‎, ‎a comparison via a simulation study is done with similar classical intervals obtained before.

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