According to the IRS, 2012 tax returns showed an average refund of $2891 with a

Question

According to the IRS, 2012 tax returns showed an average refund of $2891 with a standard deviation of $2566. Assume that 2012 tax return amounts are normally distributed. Based on this information (and information in Q7-13), generate excel output in the given space on the Tax sheet in this workbook to answer the following questions. Each orange numerical answer cell MUST reference Excel output cells in the Tax sheet.

-Find the probability a randomly selected 2012 tax return showed an amount less than or equal to $4,067 or greater than $5,234.

-Find the probability a randomly selected 2012 tax return showed an amount less than $13.

-find the probability a randomly selected 2012 tax retunr showed an amount no less than $2,664 and at most $5,294.

Not sure if I have done the graph right, but can someone explain how to use excel to get the answers and make any corrections to my table and why it was wrong? thank you
.

Normal mu 2891 sigma 2566 xi P(X<=xi) Q 7 4067 0.6766 Q 7 5234 0.8194 Q 8 13 0.1310 Q 9 2664 0.4648 Q 9 5294 0.8255 Q 10 3289 0.5616 P(X<=xi) xi Q 11 0.24 1078.6276 Q 12 0.23 995.1190 Q 13 0.75 4621.7407

Explanation / Answer

The probability a randomly selected 2012 tax return showed an amount less than or equal to $4,067 or greater than $5,234.

P(X<=4067 or X>5234) = 1 - P(4067 < X <=5234)

= 1 - [ P(X<=5234) - P(X<4067)]

= 1 - 0.8255 + 0.6766

= 0.8511

The probability a randomly selected 2012 tax return showed an amount less than $13.

P(X<13) = 0.1310

The probability a randomly selected 2012 tax retunr showed an amount no less than $2,664 and at most $5,294.

P(2664<X<5294) = P(X<5294) - P(X<2664)

= 0.8255 - 0.4648 = 0.3607

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