Repair Credit Score

Question: Normal distribution statistics problem. best answer 10 points!?

Find z

The Credit Score of a 35 year old applying for a mortgage at Ulysses Mortgage Associates is
normally distributed with a mean of 600 and a standard deviation of 100.

(a) Find the Credit Score that defines the upper 5 percent.

(b) Seventy-five percent of the customers will have a Credit Score higher than what value?

(c) Within what range would the middle 80 percent of credit scores lie?

Show your work clearly.

Answer: a) From the Normal probability tables, the z such that the area above z is 5 percents is 1.64.
z=(x-mean)sd
1.64 = (x-600)/100
164=x-600
x=764

b)The z such that the area above z is 0.75 is -0.67
-0.67=(x-600)/100
-67=x-600
x=600-67=533

c)The are to the right of 0 is 40 % and the area to the left of 0 is 40 %. The mid-80 z values are (-1.28,1.28)
-1.28=(x-600)/100
-128=x-600
x=472
1.28=(x-600)/100
128=x-600
x=728
(472,728) lie in the middle 80 %.

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