The amount requested for home loans followed the normal distribution with a mean of $70,000 and a standard deviation of $20,000
A. How much is requested on the largest 3 percent of the loans?
B. How much is requested on the smallest 10 percent of the loans?
(1) Look at your Normal Cumulative Tables to find the Z value of 97% (or 0.97). This is 100% minus the 3% for the largest. The Z value should be 1.88.
Since this Z value is standardized, we just turn it around to make it fit our numbers. X~N(70000, 20000^2)
1.88 = [X - 70000] / 20000
==> 1.88 * 20000 = X – 70000
==> X = 107615.87
(2) Now find the Z Cumulative value for .10 [This represents 10% and everything smaller]. Should be -1.28.
So take our Z value, and again change this to find our distribution X~N(70000,20000^2)
So
-1.28 = [X - 70000] / 20000
==> -1.28 * 20000 = X – 70000
==> X = 44400
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