## ABSTRACT

Imagine a binomial population consisting of an infinite number of tosses of an unbiased coin. Suppose we select samples of four tosses (n = 4) from such a population, and we continue to select such samples until we have drawn an indefinitely large number. Each sample of four coins will contain either 0 tails,

9.1 SAMPLING DISTRIBUTIONS BASED ON BINOMIAL POPULATIONS 167

1 tail, 2 tails, 3 tails, or 4 tails; there are, then, five possible outcomes. In the last chapter we showed how the relative frequency, or probability, of each of these outcomes can be determined from the expansion of (p + q)4 • Once these relative frequencies have been calculated they can be used to construct a histogram representing the expected sampling distribution of heads or tails.