Normal approximation to the error distribution
If the sample size, n, is large enough, the binomial distribution is approximately normal, so we have the approximation
error = p − π ~ normal (0, )
You will see later that it is often easier to use this normal approximation than the binomial distribution.
Closeness of the normal approximation
The following examples illustrate how the standard error is found and show the normal approximation to the error distribution.
Examples