The empirical Bayes modeling approach--latent ability random sampling in the item response theory (IRT) context--to the IRT modeling of psychological tests is described. Under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test. Three theorems are developed to establish the asymptotic posterior normality of latent variable distributions. Implications of the results are discussed. An appendix contains proofs of the theorems, in terms of proof of convergence in probability, proof of strong convergence, and proof of convergence in manifest probability. A 16-item list of references is included. (SLD)