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# Statistics : Sampling Didtributions and Probabilities

Americans have become increasingly concerned about the rising cost of Medicare. In 1990, the average annual Medicare spending per enrollee was \$3267; in 2003, the average annual Medicare spending per enrollee was \$6883 (Money, Fall 2003). Suppose you hired a consulting firm to take a sample of fifty 2003 Medicare enrollees to further investigate the nature of expenditure. Assume the population standard deviation for 2003 was \$2000.

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

b. Determine the probability the sample mean will be within ±\$300 of the population mean.

c. Determine the probability the sample mean will be greater than \$7500. 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?

#### Solution Summary

Sampling Distributions and Probabilities are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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