Given a population (maybe the population of all voters) and given a subpopulation (maybe all voters who favor candidate A) the goal of statistical sampling is to determine what percentage of the population is in the subpopulation. This percentage is known as the population proportion, denoted p.

When you take a sample you hope the percentage p^ (called the sample proportion) of members of your sample which are in the subpopulation will be close to the proportion p for the whole population. Sometimes it will be but sometimes it won't be.

What you want to know is: how often is the sample proportion p^ close to the population proportion p? To answer this we can look at the histogram of all possible samples with a specified sample size. This webform draws the histogram for all possible samples of size s taken from a population of size N where the subpopulation of interest has size m.

The output is the histogram for the sampling distribution for samples of size s taken from a population of size N with a population proportion p = m/N. (So if you know your population proportion p and population size N, then m = p*N.)

Requirements: 0 < N < 10^10, 0 < s <= N, 0 <= m <= N.