Sets bounded by random variables that are functions of the firstk, k<n, members of a random sample ofnmembers from a normal distribution are studied. These sets have the property that, before the random sample is drawn, the probability is 1 − α, 0 <a< 1, that they contain a point whose coordinates are specified functions of all of thenmembers of the random sample. Usually, these specified functions will be estimates of the distribution parameters. After numerical values are obtained for thekmembers of the subsample, the set is fixed and affords a regional forecast along with an index of the reliance to be placed on the forecast for the eventual parameter estimate which will be based on allnmembers of the random sample. Such sets and indices are called “forecast sets” and “forecast coefficients,” respectively.