If students are to understand inferential statistics successfully, they must have a profound understanding of the nature of the sampling distribution. Specifically, they must comprehend the determination of the expected value and standard error of a sampling distribution as well as the meaning of the central limit theorem. Many students in a high school or college introductory statistics class (including those taking AP Statistics) do not have the mathematical background to understand the derivation of these concepts. Consequently, they tend to memorize the results. Such a rote approach leads to a less than satisfactory understanding of inference--and can be boring. To overcome these problems, the authors, working independently, found that using simulations and combining them with a discovery approach gives students a means to discover the concepts associated with sampling distributions. One author used statistical software to conduct the activity discussed in this article; the other used a graphing calculator. Both approaches are presented for use by teachers of introductory statistics courses. (Contains 2 tables and 14 figures.)