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Question \#3: A business has three offices in a certain country, each office is staffed by two employees. The staff's yearly salaries ( 1000 s of dollars) are 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 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 c) How does E(X) from parts (a) and (b) compare to the population mean salary ? Question \#4: The National Health Statistics Reports dated Oct. 22, 2008, stated that for a sample size of 277 18-year-old American males, the sample mean waist circumference was 86.3cm. A somewhat complicated method was used to estimate various population percentiles, resulting in the following values: a) Is it plausible that the waist size distribution is at least approximately normal? Explain your reasoning. If your answer is no, conjecture the shape of the population distribution. b) Suppose that the population mean waist size is 85cm and that the population standard deviation is 15cm. How likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3cm ? c) Referring back to (b), suppose now that the population mean waist size in 83cm. Now what is the (approximate) probability that the sample mean will be at least 87.2cm ? In light of this calculation, do you think that 83cm is a reasonable value for