- Use a normal distribution to describe sampling variability.
sampling distribution of a sample proportion
A normal distribution can be used to describe the sampling distribution of a sample proportion as long as the sample size is large enough:
[latex]np \geq 10[/latex] and [latex]n(1-p) \geq 10[/latex]
The center of the sampling distribution will be equal to the value of the population proportion, [latex]p[/latex].
The standard error can be used to describe the spread of the sampling distribution. When the population proportion is known, the standard error calculated using the following formula is the standard deviation of the sampling distribution.
[latex]SE = \sqrt{\frac{p(1-p)}{n}}[/latex]