Question 1118358: The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, where the amount requested for home loans followed the normal distribution with a mean of $66,000 and a standard deviation of $20,000. (Round z-score computation to 2 decimal places and the final answers to the nearest whole dollars.)
a. What is the minimum amount requested on the largest 8% of loans?
$67,600 (wrong)
b. What is the maximum amount requested on the smallest 11% of loans?
$63,800 (wrong)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! z = (x-m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard devition.
in your problem, you need to find the critical z-score and then find the raw score that corresponds to it.
m = 66,000
s = 20,000
z is the critical z-score.
x is what you want to find.
to find the minimum amount on the largest 8% of loans, you need to find the area under the normal distribution curve that is to the left of the high critical z-score.
since .08 is to the right of it, you need to find 1 - .08 = .92 area to the left of it.
to find the maximum amount on the smallest 11% of loans, you need to find the .11 area under the normal distribution curve that is to the left of the low critical z-score.
you can use a z-score table or you can use a z-score calculator.
calculator is easier.
i used http://stattrek.com/online-calculator/normal.aspx because it works similar to how you would look up the z-score in the z-score table, but it's more accurate.
for the minimum critical z-score of the top 8%, i looked up the z-score for an area of 1 - .08 = .92 to the left of the high critical z-score.
the calculator told me that the high critical z-score = 1.405.
i rounded this to 1.41 as required.
for the maximum z-score of the bottom 11%, i looked up the z-score for an area of .11 to the left of it.
the calculator told me that the low critical z-score = -1.227.
i rounded this to -1.23 as required.
once i got the critical z-scores, i could then find the critical raw scores by using the z = (x-m) / s formula.
the minimum z-score of the top 8% was equal to 1.41.
i plugged that into the z-score formula and got:
1.41 = (x - 66,000) / 20,000.
i then solved for x to get x = 1.41 * 20,000 + 66,000 = 94,200.
the maximum z-score of the bottom 11% was equal to -1.23.
i plugged that into the z-score formula and got:
-1.23 = (x - 66,000) / 20,000.
i then solved for x to get x = -1.23 * 20,000 + 66,000 = 41,400.
below are my inputs and outputs for the high critical z-score.
below are my inputs and outputs for the low critical z-score.
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