TBJD Inc, a large government contract consulting firm

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TBJD Inc, a large government contract consulting firm, employs over 13,000 people nationwide. It has been claimed by the company that the mean age of all of its employee's is 46.7 years with a standard deviation of 7.6 years. Corporate management is considering a new healthcare package and the insurance carrier that has been selected to underwrite this insurance wants to sample 110 employees for their age before quoting a price.

1) Describe the sampling distribution of the sample mean in terms of:

a) the numerical value of its mean,

b) the numerical value of its standard error of the mean and,

c) its shape (and you must explain why).

2) Suppose that a single random sample of size n=110 employees is selected. What is the chance that the mean of the sample will be within 1.5 years either way of the population mean? That is, what is the chance that the sample mean will be in range between 45.2 and 48.2 years?

3) For the sample that was selected in part 2, calculate the average age. On the basis of the TBJD-supplied data, what is the chance of drawing a sample whose mean would be that large or larger?

4) On the basis of the probability calculated in part 3, what conclusion, if any, can be reached about the truthfulness of the consulting firms claim about mean employee age? Explain.