Question

A group of students got the following scores in an achievement test:9,12,15,18,21 and 24 . consider the sample of size 3 that can be drawn from this population. Construct a sampling distribution of the resulting means and find the probability

Answer 1

The number of possible samples of size n=3 from a population of size N=6 is,

$=C_6^3= \binom{6}{3}=20$

The sample means are derived from the formula, $\bar x_i={\sum x_i\over3}$

The samples and their means are shown in the table below

The sampling distribution is as follows:

$\begin{matrix}{\bar x_i}&{12}&{13}&{14}&{15}&{16}&{17}&{18}&{19}&{20}&{21}\\{p(\bar x_i)}&{\frac{1}{{20}}}&{\frac{1}{{20}}}&{\frac{1}{{10}}}&{\frac{3}{20}}&{\frac{3}{{20}}}&{\frac{3}{20}}&{\frac{3}{{20}}}&{\frac{1}{10}}&{\frac{1}{{20}}}&{\frac{1}{{20}}}\end{matrix}$