. According to the Internal Revenue Service, the average length of time for an i

Question

. According to the Internal Revenue Service, the average length of time for an individual to complete (keep records for, learn, prepare, copy, assemble, and send) IRS Form 1040 is 10.53 hours (without any attached schedules). The distribution is unknown. Let us assume that the standard deviation is two hours. Suppose we randomly sample 36 taxpayers. a. In words, = _____________ b. In words, X ¯ = _____________ c. X ¯ ~ _____(_____,_____) d. Would you be surprised if the 36 taxpayers finished their Form 1040s in an average of more than 12 hours? Explain why or why not in complete sentences. e. Would you be surprised if one taxpayer finished his or her Form 1040 in more than 12 hours? In a complete sentence, explain why

Explanation / Answer

X represents the time taken by an individual to complete the form 1040

X' represents the average time taken by an individual to complete the form 1040

X' will be approximately N(10.52,SD/sqr(n)) = N(10.53,1/3)

Since the time taken 12 hours will be more than three times the standard deviation of the normal distribution, hence i will be suprised if somebody takes more than 12 hours to fill the form 1040

No, for single tax payer, the SD = 2 hours, hence the time taken will be (10.53+2) = 12.53 is also optimal, hence it will not be a suprise if somebody single person took more than 12 hours to fill the form

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