## 4.3 Population distribution unknown and \(n < 30\)

If the underlying distribution is unknown, and the sample size is small (i.e. \(n < 30\)), then it is not possible to apply the Central Limit Theorem. In this situation, the distribution of the sample mean is unknown.

For example, suppose a random sample of \(n = 20\) is taken from from a population with unknown distribution that has with \(\mu = 5\) and \(\sigma^2 = 1\), and a sample mean is calculated. In this situation, it is not possible to determine the distribution of \(\overline{X}\).

**Your turn:**

The distribution is unknown