Probability that sample mean will be within plus or minus

Reference no: EM13117703

Americans have become increasingly concerned about the rising costs of Medicare. In 1990, the average annual Medicare spending per enrollee was $3,267; in 2003, the average annual Medicare spending per enrollee was$6,883. Suppose you hired a consulting firm to take a sample of fifty 2003 Medicare enrollees to further investigate the nature of expenditures. Assume the population standard deviation for 2003 was $2,000

a. Show the sampling distribution of the mean amount of Medicare spending for a sample of fifty 2003 enrollees.

b. What is the probability the sample mean will be within, plus or minus, $300 of the population mean?

c. What is the probability that the sample mean will be greater than $7,500? If the consulting firm tells you the sample mean for the Medicare enrollees they interviewed was $7,500 would you question whether they followed correct simple random sampling procedures? Why or why not?

Reference no: EM13117703

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