ABSTRACT
If a random variable X has a binomial distribution, then for large n the random variable X/n is approximately normally distributed with mean p and standard deviation equal to the square root of pQ/n. If n is the size of a random sample from a population in which p is the proportion of elements classified as “success” because of the possession of a specified characteristic, then the large sample distribution of X/n, the sample proportion having the specified characteristic, serves as the basis for constructing a confidence interval for p, the corresponding population proportion. By “n is large” it is meant that np and n(1 – p) are both greater than 5.
