Given the data: 123, 126, 129, 132, and (a) construct a sampling of the mean (b) draw a histgyfor the sample means

a) We construct the probability distribution of the sample mean for samples of size two drawn from the population of four numbers.

$\def\arraystretch{1.5} \begin{array}{c:c} Sample\ point & mean,\bar{X} \\ \hline 123,126 & 124.5 \\ \hdashline 123,129& 126 \\ \hdashline 123,132 & 127.5 \\ \hdashline 126,129& 127.5 \\ \hdashline 126,132& 129 \\ \hdashline 129,132& 130.5 \\ \hdashline \end{array}$

$\def\arraystretch{1.5} \begin{array}{c:c} x & 124.5 & 126 & 127.5 & 129 & 130.5 \\ \hline p(x) & 1/6 & 1/6 & 1/3 & 1/6 & 1/6 \end{array}$

b)