The family of Weibull distributions was investigated as a model for the distributions of response times for items in computer-based criterion-referenced tests. The fit of these distributions were, with a few exceptions, good to excellent according to the Kolmogorov-Smirnov test. For a few relatively simple items, the two-parameter gamma distribution provided better fits. The three parameters of the Weibull distribution were as follows: the location parameter represents the theoretical minimum time required; the scale parameter is related to the mean; and the shape parameter (c) is related to two kinds of difficulty indices. It also appeared that the shape parameter was related to the degree of familiarity of the item and the degree of engagement or involvement of the test takers. A function related to c was the conditional response rate, which is called the hazard rate in system-reliability literature. The c parameter was found to be sensitive to the conceptual difficulty of items that were equal according to traditional difficulty indices. An index was developed for the efficiency of lessons and this, too, was found to be related to the Weibull parameter. Finally, c was judged to be related to the optimal cutoff point for criterion-referenced tests. (Author/CTM)