Americans have become increasingly concerned about the rising cost of Medicare.

Question

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 $6285 (Money, Fall 2003). Suppose you hired a consulting firm to take a sample of 45 Medicare enrolless from 2003 to further investigate the nature of expenditure. Assume the population standard deviation for 2003 was $2320.

What is the probability the sample average Medicare spending is at least $5821?

Explanation / Answer

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 $6285 (Money, Fall 2003). Suppose you hired a consulting firm to take a sample of 45 Medicare enrolless from 2003 to further investigate the nature of expenditure. Assume the population standard deviation for 2003 was $2320.What is the probability the sample average Medicare spending is at least $5821?

Mean in 2003 =   6285

Sd =2320

Z value for 5821, z=(5281-6285)/2320 = -0.43

P( x >=5821) = P( z >= -0.43) = 0.6664

The required P= 0.6664

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