Answer to Question #52678 in Quantitative Methods for Langa

Question

an inland revenue services (IRS) regional office in the United States has plotted a large sample of tax refund amounts and found that they form a bell-shaped distribution symmetrical about the central line. The average refund amount was found to be close to $750 with a standard deviation of $125. Most refund values are fairly close to the central line,suggesting normal distribution.
The regional office is especially interested in the largerefunds. A refund larger than $1000 is considered large, and the office would
like to know what percentage of current funds based on the normal distribution
are in excess of this amount.
A second question involves the office’s concern with newwithholding guidelines for taxpayers. It has been estimated that the average
refund amount will rise by $120 after these guidelines go into effect, and the
IRS office wonders how the percentage of large refunds will be affected.

1. Calculatedthe percentage of refunds expected to exceed $1000 under the current
withholding guidelines

2. Calculate the percentage increase in therefund exceeding $1000 if the average refund increases by $120. Assume that the
degree of variability in refund amounts remain unchanged when the average
refund increases.

3. What wouldbe the effect on the percentage of refunds over $1000 if the average refund
amount actually drops by $70

4. Whatchange in the current average refund over $1000 will produce a 5% increase in
the current percentage of refunds over $1000. (Assume no change in the degree of
variability in refunds amounts.)

Answer 1

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