Sample Proportion

Let there be  successes out of  Bernoulli trials. The sample proportion is the fraction of samples which were successes, so

(1)

For large ,  has an approximately normal distribution. Let RE be the relative error and SE the standard error, then

			(2)
			(3)
			(4)

where CI is the confidence interval and  is the erf function. The number of tries needed to determine  with relative error RE and confidence interval CI is