Equity Home Loans

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

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?

Public Comments

1. (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. 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.