8. + 2.63(10 points | Prevous Newers Devorestat5P042. My NotesAsk Your Te A comp

Question

8. + 2.63(10 points | Prevous Newers Devorestat5P042. My NotesAsk Your Te A company maintains three offices in a certain region, each staffed by two employces. Information concerning yearly salaries (100s of dollars) is as follows. Office Employee 12 Salary 29.533.3 30.3 33.3 25.3 29.S (a) Suppose two of these employees are randomly selected trom among the six (without replacement). Determine the sampling distribution of the sample mean salary X. (Give answrs accurate to 3 decimal places.) 27.4 27.8 29,3 29.5 29.9 31,4 31,8 33.3 p(x) | 13 |X 0.067 0.2 X 10.13 X1O.257|X 0, 13 |X|0.06 X (b) Suppose one of the three offices is randomly selected. Let X1 and X2 denote the salaries of the two employees. Determine the sampling distribution of X. (ive ansers accurate to 3 decimal places.) 27.4 31.4 31.8 (c) How does E(X) from pdrls (a) and (b) cumpare to the population rnean salary ? E(X) from part (a) is | equal to -v, and E(X) from part (b) i5 | equal to

Explanation / Answer

from above given data: as P(Xbar) =P(X1)*P(X2) for which xbar =(X1+X2)/2

hence below is probability distribution:

b) for probability to select each offfice is 1/3

hence

xbar 27.4 27.8 29.3 29.5 29.9 31.4 31.8 33.3 p(xbar) 0.133 0.067 0.133 0.067 0.133 0.267 0.100 0.100

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