Question

A population consists of the numbers 2, 4, 8, 10 and 5. Let us list all the possible samples of size 3 from this population and construct the sampling distribution of the sample mean.

Answer 1

A population consists of the numbers 2, 4, 8, 10 and 5

Sampling distribution of size 3 can be given as

$P(\bar X=4.66) = \dfrac{1}{5}$

$P(\bar X=6.66) = \dfrac{1}{10}$

$P(\bar X=5.66) = \dfrac{1}{10}$

$P(\bar X=5) = \dfrac{1}{5}$

$P(\bar X=7.33) = \dfrac{1}{10}$

$P(\bar X=6.33) = \dfrac{1}{10}$

$P(\bar X=3.66) = \dfrac{1}{10}$

$P(\bar X=7.66) = \dfrac{1}{10}$