Because the test information function and its two modified formulas provide useful information, the reliability coefficient of a test is no longer necessary in modern mental test theory. Yet it is interesting to know how to predict the coefficient using the test information function and its modifications, tailored for each separate population of examinees. In the process, it becomes apparent that the traditional concept of test reliability is misleading, for without changing the test the coefficient can be drastically different if the population of examinees changes. To illustrate, six ability distributions are hypothesized, and predictions of their tailored reliability coefficients and tailored standard errors of measurement are made. Using Monte Carlo methods, a simulation study produced a response pattern for each hypothetical subject for each of the test and retest situations. These examples make the differences among the separate ability distributions and among the three predicted indices for each ability distribution clearly visible. Five tables and three graphs are included. (SLD)