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:

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

$\overline{X}$ ?

$\overline{X} \sim$ ...

N(7, 0.125) N(7, 0.3125) The distribution is unknown N(7, 6.25)

The distribution is unknown

4.3 Population distribution unknown and n<30n < 30

0 of 1 correct

4.3 Population distribution unknown and $n < 30$