A company maintains three offices in a certain region, each staffed by two emplo

Question

A company maintains three offices in a certain region, each staffed by two employees. Information concerning yearly salaries (1000s of dollars) is as follows: Office Employee 1 56 Salary 30.7 34.6 31.2 34.6 26.8 30.7 (a) Suppose two of these employees are randomly selected from among the six (without replacement). Determine the sampling distribution of the sample mean salary X. (I Enter your answers for p(R) as fractions.) 28.75 30.70 30.95 32.65 34.60 P(x) x 15 15 (b) Suppose one of the three offices is randomly selected . Let X and X denote the salaries of the two employees. Determine the sampling distribution of X. (Enter your answers as fractions .) 28.25 32.65 32.90 p(x)

Explanation / Answer

a)

b)

probability for each of them would be 1/3 because we can select (1,2), (2,1), (3,4), (4,3), (5,6), (6,5)

Sample Average (1,2) 32.65 (1,3) 30.95 (1,4) 32.65 (1,5) 28.75 (1,6) 30.7 (2,1) 32.65 (2,3) 32.9 (2,4) 34.6 (2,5) 30.7 (2,6) 32.65 (3,1) 30.95 (3,2) 32.9 (3,4) 32.9 (3,5) 29 (3,6) 30.95 (4,1) 32.65 (4,2) 34.6 (4,3) 32.9 (4,5) 30.7 (4,6) 32.65 (5,1) 28.75 (5,2) 30.7 (5,3) 29 (5,4) 30.7 (5,6) 28.75 (6,1) 30.7 (6,2) 32.65 (6,3) 30.95 (6,4) 32.65 (6,5) 28.75 Total 30 instances x Counts P(x) 32.65 8 4/15 30.95 4 2/15 28.75 4 2/15 32.90 4 2/15 34.60 2 1/15 30.70 6 3/15 29.00 2 1/15

b)

probability for each of them would be 1/3 because we can select (1,2), (2,1), (3,4), (4,3), (5,6), (6,5)

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