Answer to Question #299099 in Statistics and Probability for Cha

Question #299099

Given the data: 123, 126, 129, 132, and (a) construct a sampling of


the mean (b) draw a histgyfor the sample means


1
Expert's answer
2022-02-18T15:45:47-0500

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


Sample pointmean,Xˉ123,126124.5123,129126123,132127.5126,129127.5126,132129129,132130.5\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}

x124.5126127.5129130.5p(x)1/61/61/31/61/6\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)


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