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QUESTION

For a certain income level, the IRS knows that the amounts claimed for Medical Deductions (X1 ), Charitable Contributions (X2 ), and Miscellaneous

For a certain income level, the IRS knows that the amounts claimed for Medical Deductions (X1 ), Charitable Contributions (X2 ), and Miscellaneous Deductions (X3), are Independent Normally distributed variables with means $400,$800, and $100 and standard deviations$100, $250, and$40 respectively.

a) What is the probability that the amount claimed for these 3 deductions is less that $1600? b) If someone, from this income level, reports on his return a total of$2100 for these deductions, how likely is this or a larger amount? Justify your answer!