A mortgage company classifies its borrowers into three categories: Low Risk, Med

Question

A mortgage company classifies its borrowers into three categories: Low Risk, Medium Risk, and High Risk. From experience, the company knows that:

2% of low risk borrowers eventually default on their mortgages.

9% of medium risk borrowers eventually default on their mortgages.

13% of high risk borrowers eventually default on their mortgages.

The mortgages for 116 high risk borrowers are put together into one portfolio. The company determines that they will profit on the portfolio as long as no more than 19% of borrowers with mortgages in the portfolio default. What is the probability that the company makes a profit on the portfolio?

Explanation / Answer

here point estimate p=0.13

for n=116 ; std error =(p(1-p)/n)1/2 =0.0312

hence P(X<0.19)=P(Z<(0.19-0.13)/0.0312)=P(Z<1.9216)=0.9727

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