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	1	1	2	2	3	3
Employee	1	2	3	4	5	6
Salary	33.7	37.6	34.2	37.6	29.8	33.7

(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.

(Enter your answers for p(x) as fractions.)

x	31.75		33.70	33.95	35.65		37.60
p(x)		1 15				2 15

(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.

(Enter your answers as fractions.)

x	31.75	35.65	35.90
p(x)

(c) How does

E(X)

from parts (a) and (b) compare to the population mean salary ?

E(X)

from part (a) is ---Select--- greater than less than equal to , and

E(X)

from part (b) is ---Select--- greater than less than equal to .

The inside diameter of a randomly selected piston ring is a random variable with mean value9cm and standard deviation0.02cm. Suppose the distribution of the diameter is normal. (Round your answers to four decimal places.)(a) Calculate

P(8.99X9.01)

whenn= 16.

P(8.99X9.01)

= (b) How likely is it that the sample mean diameter exceeds9.01whenn= 25?

P(X9.01)

=