the credit score of a 35 year old boy applying for a mortgage atulysses Mortgage

Question

the credit score of a 35 year old boy applying for a mortgage atulysses Mortgage associates is normally distributed with a mean 600and 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 scorehigher than what value?
c) Within what range would the middle 80 percent of credit scoreslie?

Explanation / Answer

(a) From the Normal probability tables, the z such that the areaabove z is 5 percents is 1.64. z=(x-)/sd --> 1.64 = (x-600)/100 --> 164=x-600 So 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 So x=600-67=533 c)The are to the right of 0 is 40 % and the area to the left of 0is 40 %. The mid-80 z values are (-1.28,1.28) --> -1.28=(x-600)/100 --> -128=x-600 So x=472 1.28=(x-600)/100 --> 128=x-600 So x=728 (472,728) lie in the middle 80 %.

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