On a peer to peer (P2P) lending website, borrowers complete an approval scoring form that lenders use to assess creditworthiness Lenders generally believe that borrowers who score at least 73 do not default on loans Consequently, borrowers are rated A if their overall score is at least 73 , otherwise they are rated B A reasonably large sample of real borrower data was collected among those that did not default on their loans, initial approval scores were normally distributed with a mean of 77 9 and a standard deviation of 6 7 among those that defaulted on their loans, initial approval scores were normally distributed with a mean of 66 7 and a standard deviation of 9 8 What proportion of borrowers that a) defaulted were initially rated A b) did not default were initially rated B c) defaulted were miscategorized initially d) did not default were miscategorized initially Among those that defaulted, what is the probability that a borrower a) scored above 74 1 b) scored below 60 5 or above 80 6 c) was rated B and scored above 52 7 d) was rated A and scored below 74 1 e) was rated A given scored above 66 7 f) scored below 66 7 given rated B

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jul 06, 2024

On a peer-to-peer (P2P) lending website, borrowers complete an approval scoring form that lenders use to assess creditworthiness. Lenders generally believe that borrowers who score

On a peer-to-peer (P2P) lending website, borrowers complete an approval scoring form that lenders use to assess creditworthiness. Lenders generally believe that borrowers who score at least 73 do not default on loans. Consequently, borrowers are rated A if their overall score is at least 73, otherwise they are rated B. A reasonably large sample of real borrower data was collected:

among those that did not default on their loans, initial approval scores were normally distributed with a mean of 77.9 and a standard deviation of 6.7.
among those that defaulted on their loans, initial approval scores were normally distributed with a mean of 66.7 and a standard deviation of 9.8.
What proportion of borrowers that:
a) defaulted were initially rated A? b) did not default were initially rated B? c) defaulted were miscategorized initially? d) did not default were miscategorized initially?
Among those that defaulted, what is the probability that a borrower: a) scored above 74.1? b) scored below 60.5 or above 80.6? c) was rated B and scored above 52.7? d) was rated A and scored below 74.1? e) was rated A given scored above 66.7? f) scored below 66.7 given rated B?