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MAT 133: Ch 8 Review WS, p.4 6. The average yearly Medicare Hospital Insurance benefit per person was $4064 in a recent year with a standard deviation of $460. A medical care researcher gathers a random sample of 40 Medicare patients from the population of 44 million Medicare users. a. Verify that the conditions of the Central Limit Theorem for Means are met. b. Describe the sampling distribution of the sample mean. (Give shape, center, and spread using symbols and with explanations or formulas as necessary; Give 4 decimal places) (For parts c & d - Shade and label appropriately; Give 4 decimal places and P(X) notation from StatCrunch, circling the answer) c. There is a 85% chance the mean amount of Medicare hospital Insurance benefit for a group of 40 random Medicare patients is at or above (Give units) d. Would it be unusual for the mean Medicare Hospital Insurance benefit for a random group of 40 Medicare patients to be less than $3900? Explain using probability