jane


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?

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2 Responses to “The amount requested for home loans followed the normal distribution with a mean of $70,000 and a standard dev”

1. Jeff Lebowski on February 24th, 2009 12:42 pm

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   (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

2. vlee1225 on February 25th, 2009 5:46 pm

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   let x = loan in thousands
   the normalized variable is z = (x - 70)/20

   A. the largest 3% is when
   Prob( z >1.89) = 97%
   or (x - 70)/20 > 1.89
   x - 70 > 20(1.89) = 37.8
   x > 107.8
   the largest 3% of loans are from 107.8 thousands and up

   B. the smallest 10 % is when
   Prob (z < -1.29) = 10%
   (x - 70)/20 < -1.29
   x - 70 < - 25.8
   x < 44.2
   the last 10 % of loans are those $44.2 thousands or lower.