A company maintains three offices in a certain region, eachstaffed by two employees. Information concerning yearly salaries(1000s of dollars) is as follows:
| Office | 1 | 1 | 2 | 2 | 3 | 3 |
| Employee | 1 | 2 | 3 | 4 | 5 | 6 |
| Salary | Â Â 26.7Â Â | Â Â 30.6Â Â | Â Â 27.2Â Â | Â Â 30.6Â Â | Â Â 22.8Â Â | Â Â 26.7Â Â |
(a) Suppose two of these employees are randomly selected fromamong the six (without replacement). Determine the samplingdistribution of the sample mean salary
X.
(Enter your answers for p(x) asfractions.)
| x    | 24.75 | | 26.70 | 26.95 | 28.65 | | 30.60 |
| p(x)Â Â Â Â | Â Â Â Â Â Â | Â Â Â Â | Â Â Â Â Â Â | Â Â Â Â Â Â | Â Â Â Â Â Â | Â Â Â Â | Â Â Â Â Â Â |
(b) Suppose one of the three offices is randomly selected. LetX1 and X2 denote thesalaries of the two employees. Determine the sampling distributionof
X.
(Enter your answers as fractions.)
| x | 24.75 | 28.65 | 28.90 |
| p(x)Â Â Â Â | Â Â Â Â Â Â | Â Â Â Â Â Â | Â Â Â Â Â Â |
(c) How does
E(X)
from parts (a) and (b) compare to the population mean salaryμ?
E(X)
from part (a) is  ---Select--- greater than less thanequal to μ, and
E(X)
from part (b) is  ---Select--- greater than less thanequal to μ.
