SOLUTION: The average refund amount was 748 with a standard deviation of 124. Standard normal distribution 1. Calculate the percentage of refunds expected to exceed 1000 under the current

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Question 773397: The average refund amount was 748 with a standard deviation of 124. Standard normal distribution
1. Calculate the percentage of refunds expected to exceed 1000 under the current witholding guidelines.
2. Calculate the percentage increase in the refunds exceeding 1000 if the average refunds invreases by 150. assume that the degree of variability in refunds remain unchanged when the average refund increases by 150.
3. What would be the effect on the percentage of refunds over 1000 if the average refund amount actually drops by 75.
4. What change in the current average refund over 1000 will produce a 7% increase in the current percentage of refunds over 1000. Assume no change in the
degree of variability in refund amounts.
please show all workings.
Thanks

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The average refund amount was 748 with a standard deviation of 124. Standard normal distribution
1. Calculate the percentage of refunds expected to exceed 1000 under the current witholding guidelines.
z(1000) = (1000-748)/124 = 2.0323
P(x > 1000) = P(z > 2.0323) = 0.0211 = 2.11%
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2. Calculate the percentage increase in the refunds exceeding 1000 if the average refunds invreases by 150. assume that the degree of variability in refunds remain unchanged when the average refund increases by 150.
z(1000) = (1000-898)/124 = 0.8226
P(x > 1000) = P(z > 0.8226) = 0.2054 = 20.54%
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3. What would be the effect on the percentage of refunds over 1000 if the average refund amount actually drops by 75.
I'll leave that to you.
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4. What change in the current average refund over 1000 will produce a 7% increase in the current percentage of refunds over 1000. Assume no change in the
degree of variability in refund amounts.
----
invNorm(0.93) =
(1000+x - 748)/124 = 1.4758
----
1000+x = 1.4758*124 + 748
1000+x = 931
x = -$69.00
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Chers,
Stan H.
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