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

We have given the population $2,4,8,10$ and $5.$

Sampling distribution of size 3 can be given as

Sampling distribution of sample mean,

$P(\bar X=4.66) = \dfrac{1}{5} ,$ $P(\bar X=3.66) = \dfrac{1}{10},$

$P(\bar X=6.66) = \dfrac{1}{10},$ $P(\bar X = 7.66) = \dfrac{1}{10},$

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

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

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

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