The sampling distribution of the sample mean is shown below. $$\begin{array} { c | c c c c c }
\overline { \mathrm { x } } & 4 & 5 & 6 & 7 & 8 \
\hline \mathrm { p } ( \overline { \mathrm { x } } ) & 1 / 9 & 2 / 9 & 3 / 9 & 2 / 9 & 1 / 9
\end{array}$$ Find the expected value of the sampling distribution of the sample mean.
A) 4
B) 5
C) 6
D) 7

Question

The sampling distribution of the sample mean is shown below. $$\begin{array} { c | c c c c c } 
\overline { \mathrm { x } } & 4 & 5 & 6 & 7 & 8 \
\hline \mathrm { p } ( \overline { \mathrm { x } } ) & 1 / 9 & 2 / 9 & 3 / 9 & 2 / 9 & 1 / 9
\end{array}$$ Find the expected value of the sampling distribution of the sample mean.
A) 4
B) 5
C) 6
D) 7

Quizplus · Accepted Answer

The expected value is calculated by multiplying each sample mean by its probability and summing the results: (4)(1/9) + (5)(2/9) + (6)(3/9) + (7)(2/9) + (8)(1/9) = 6.

The Sampling Distribution of the Sample Mean Is Shown Below