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 75 do not default on loans. Consequently, borrowers are rated A if their overall score is at least 75, otherwise they are rated B. A reasonably large sample of real borrower data was collected: i. among those that did not default on their loans, initial approval scores were normally distributed with a mean of 80.6 and a standard deviation of 6.9. ii. among those that defaulted on their loans, initial approval scores were normally distributed with a mean of 70.9 and a standard deviation of 7.8. Report each answer as a decimal (not percent) accurate to at least 4 decimal places. Answers from software or from rounded z-scores (to 2 decimal places) are accepted. 1. What proportion of borrowers that 3) did not default were initially rated A? 0.7910 b) defaulted were initially rated B? 0.7019 c) did not default were miscategorized initially? 2090 dj defaulted were miscategorized initially? | 0.2981 2. Among those that did not default, what is the probability that a borrower. a) scored above 83.9? Ibj scored below 68.1 or above 88.5? c) was rated B and scored above 67.7? d) was rated A and scored below 83.9? e) was rated B given scored below 80.6? f) scored above 80.6 given rated A