ABSTRACT
This chapter discusses the details of how to use the normal distribution to find the proportion of individual scores in any given interval. It also discusses the binomial distribution, which is another important distribution used in statistical inference. More mathematically rigorous presentations are available in many standard probability texts. The “brute force” method for finding the number of relevant outcomes works, as we saw above, but it is cumbersome, and it becomes more so very quickly if the number of “tacks”—that is, independent trials—involved in the game increases. A binomial variable, as we saw in the previous sections, is a variable that counts the number of yeses in n independent trials. Theoretically, the continuity correction will always improve the approximation in using a normal distribution to approximate a binomial. But as a practical matter, the continuity correction will not make much difference with large n, because the bigger n gets, the narrower each individual block on the binomial distribution becomes.
