## 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 $$\overline{X}$$.

Suppose a random sample of $$n = 20$$ is taken from a population with an unknown distribution that has $$\mu = 7$$ and $$\sigma^2 = 2.5^2$$. What is the distribution of $$\overline{X}$$? $$\overline{X} \sim$$...