Americans have become increasingly concerned about the rising cost of Medicare. In 2002, the average annual Medicare spending per enrollee was $3267; in 2012, the average annual Medicare spending per enrollee was $6883 (Money Magazine). Suppose you hired a consulting firm to take a sample of 50 2012 Medicare enrollees to further investigate the nature of expenditures. Assume the population standard deviation for 2012 was $2000.

1. Describe (in concise terms) the sampling distribution of the mean amount of Medicare spending for a sample of 50 enrollees. In a sentence, convey what you know about the distribution of the sample mean for this sample.
2. What is the probability the sample mean will be within +/- $300 of the population mean?
3. What is the probability the sample mean will be greater than $7500?
4. If the consulting firm tells you the sample mean for the Medicare enrollees they interviewed was $7500, would you question whether they followed correct simple random sampling procedures? Why or why not, support your answer?