xyz grocery a large regional supermarket chain employs over 9000 people. it has been claimed by the company that the mean age of all employees is 43.7 years with a standard deviation of 7.3 years. the company is thinking of introducing a new healthcare package. the insurance carrier that has been selected to underwrite this insurance wants to sample 80 employees for their age before quoting a price.

1. Describe the sampling distribution of the sample mean in terms of

a. Numerical value of its mean

b. The numerical value of its standard error of the mean

c. Its shape ( explan why)

2. Suppose a single random sample of size n = 80 employees was actually selected. it was calculated for this sample that the average age was 45.9 years. on the basis of the company supplied data, what is the chance of drawing a sample whose mean would be this large or larger?

3. Supose that a single random same of n=84 employees was selected what is the chance that the mean of this sample will be within 1.5 years either way of the population mean? what is the chance that the sample mean will be in the range betweeen 45.2 and 48.2 years?

4. On the basis of the probability calculated in part 2 above, what conclusion if any, can be reached about the truthfulness of the supermarket chain's claim about mean employee age? explain