The capacity of short-term memory is a key constraint when people make online judgments requiring them to rely on samples retrieved from memory (e.g., Dougherty & Hunter, 2003). In this article, the authors compare 2 accounts of how people use knowledge of statistical distributions to make point estimates: either by retrieving precomputed large-sample representations or by retrieving small samples of similar observations post hoc at the time of judgment, as constrained by short-term memory capacity (the naïve sampling model: Juslin, Winman, & Hansson, 2007). Results from four experiments support the predictions by the naïve sampling model, including that participants sometimes guess values that they, when probed, demonstrably know have the lowest probability of occurring. Experiment 1 also demonstrated the operations of an unpredicted recognition-based inference. Computational modeling also incorporating this process demonstrated that the data from all 4 experiments were better predicted by assuming a post hoc sampling process constrained by short-term memory capacity than by assuming abstraction of large-sample representations of the distribution.