Relationships between Bayesian ability estimates and the parameters of a normal population distribution are derived in the context of classical test theory. Analogies are provided for use as approximations in work with item response theory (IRT). The following issues are addressed: (1) the relationship between the distribution of the latent ability variable in a population and the distribution of ability estimates; (2) how to proceed in calculating the Bayesian estimate if the population distribution is not known; and (3) how to estimate the distributions of specified subpopulations when Bayesian ability estimates have been calculated in accordance with a common population distribution. Exact relationships are derived to address these questions in the context of classical test theory, assuming normally distributed abilities and errors. The analogues that are offered are for a not-uncommon IRT context in which the researcher has software to calculate the Bayesian IRT estimates for individuals under the assumption of a normal population distribution, but possesses neither values of the population parameters nor software with which to estimate them. (Contains 1 figure and 11 references.) (SLD)