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A company maintains three offices in a certain region, each staffed by two employees. Information concerning yearly salaries (1000s of dollars) is as follows:

Office112233Employee123456Salary29.733.630.233.625.829.7\begin{array}{lcccccc} \text {Office} & 1 & 1 & 2 & 2 & 3 & 3 \\ \text {Employee} & 1 & 2 & 3 & 4 & 5 & 6 \\ \text {Salary} & 29.7 & 33.6 & 30.2 & 33.6 & 25.8 & 29.7 \end{array}

a. Suppose two of these employees are randomly selected from among the six (without replacement). Determine the sampling distribution of the sample mean salary Xˉ\bar{X}. b. Suppose one of the three offices is randomly selected. Let X1X_{1} and X2X_{2} denote the salaries of the two employees. Determine the sampling distribution of Xˉ\bar{X}. c. How does E(Xˉ)E(\bar{X}) from parts (a) and (b) compare to the population mean salary μ\mu?

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a. Determine the sample mean salary (sum of all values divided by the number of values) for each sample of 2 employees:

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