Question 1155746: A mortgage company classifies its borrowers into three categories: Low Risk, Medium Risk, and High Risk. From experience, the company knows that:
3% of low risk borrowers eventually default on their mortgages.
7% of medium risk borrowers eventually default on their mortgages.
13% of high risk borrowers eventually default on their mortgages.
The mortgages for 133 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?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 19% of 133 is 25.27, so want no more than 25 to default.
On calculator use binomcdf (133,.13,26) and probability is 0.9879. ANSWER
Can check by using probability of 26 defaulting or 133C26*.13^26*.87^107=0.0093, then probability of 27 and 28 until the numbers are too small. But given what 26 is, the other ones will be smaller and the answer is reasonable.
Normal approximation is np=17.29; np(1-p)^1/2 is sd =3.88
want probability it is less than 25.
z=(25-17.29)/3.88
=1.99
Probability z>1.99=0.0232
probability z<1.99=0.9768, with error (this is an approximation) but again close to exact answer above.
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