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: (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. (Enter your answers for p(x) as fractions.) (b) Suppose one of the three officers is randomly selected. Let X_1 and X_2 denote the salaries of the two employees. Determine the sampling distribution of X. (Enter your answers as fractions.)

Explanation / Answer

a) here as there are 6*5 =30 samples possible.

therefore probability of each sample =1/30

from above let x1 and x2 are first and second sample:

therefore

from above adding duplicate mean probability below is the probability distribution:

b)

as each office has probability of (1/3) to be selected therefore:

x1 x2 mean P(x) 38.6 34.7 36.65 1/30 35.2 34.7 34.95 1/30 38.6 34.7 36.65 1/30 30.8 34.7 32.75 1/30 34.7 34.7 34.7 1/30 34.7 38.6 36.65 1/30 35.2 38.6 36.9 1/30 38.6 38.6 38.6 1/30 30.8 38.6 34.7 1/30 34.7 38.6 36.65 1/30 34.7 35.2 34.95 1/30 38.6 35.2 36.9 1/30 38.6 35.2 36.9 1/30 30.8 35.2 33 1/30 34.7 35.2 34.95 1/30 34.7 38.6 36.65 1/30 38.6 38.6 38.6 1/30 35.2 38.6 36.9 1/30 30.8 38.6 34.7 1/30 34.7 38.6 36.65 1/30 34.7 30.8 32.75 1/30 38.6 30.8 34.7 1/30 35.2 30.8 33 1/30 38.6 30.8 34.7 1/30 34.7 30.8 32.75 1/30 34.7 34.7 34.7 1/30 38.6 34.7 36.65 1/30 35.2 34.7 34.95 1/30 38.6 34.7 36.65 1/30 30.8 34.7 32.75 1/30

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