Capture-recapture is a sampling design that is used to estimate the size of animal populations in a wilderness. A random sample of $M$ animals is captured, and the animals are tagged and released. At a later time, another random sample of $n$ animals will be recaptured and the number of tagged animals $X$ is recorded.

Given values of $M$, $n$, and $X$, we will estimate the population size $N$ using the hypergeometric probability distribution. We will then be able to approximate the hypergeometric distribution with the normal distribution. From the normal distribution, we derive a third-degree polynomial that provides a confidence interval for the unknown $N$.

To illustrate our method, we will break into groups. Each group will estimate the number of black beans in a bowl. The estimate will be in the form of a confidence interval.