According to the IRS, 2012 tax returns showed an average refund of $2439 with a
ID: 3130708 • Letter: A
Question
According to the IRS, 2012 tax returns showed an average refund of $2439 with a standard deviation of $2198. Assume that 2012 tax return amounts are normally distributed.The probability is .4 that a randomly selected 2012 tax return showed between what two amounts equidistant from the mean? Find the lower endpoint. Use the lower endpoint and some math to find the upper endpoint. According to the IRS, 2012 tax returns showed an average refund of $2439 with a standard deviation of $2198. Assume that 2012 tax return amounts are normally distributed.
The probability is .4 that a randomly selected 2012 tax return showed between what two amounts equidistant from the mean? Find the lower endpoint. Use the lower endpoint and some math to find the upper endpoint.
The probability is .4 that a randomly selected 2012 tax return showed between what two amounts equidistant from the mean? Find the lower endpoint. Use the lower endpoint and some math to find the upper endpoint.
Explanation / Answer
As the middle area is
Middle Area = P(x1<x<x2) = 0.4
Then the left tailed area of the left endpoint is
P(x<x1) = (1-P(x1<x<x2))/2 = 0.3
Thus, the z score corresponding to the left endpoint, by table/technology, is
z1 = -0.524400513
By symmetry,
z2 = 0.524400513
As
u = mean = 2439
s = standard deviation = 2198
Then
x1 = u + z1*s = 1286.367673 [LOWER ENDPOINT]
x2 = u + z2*s = 3591.632327 [UPPER ENDPOINT]
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