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 72 do not default on loans. Consequently, borrowers are rated A if their overall score is at least 72, 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 78.9 and a standard deviation of 7.5. ii. among those that defaulted on their loans, initial approval scores were normally distributed with a mean of 67.3 and a standard deviation of 10.3.2. Among those that did not default, what is the probability that a borrower: a) scored above 96.8? b) scored below 86.3 or above 100? c) was rated B and scored above 85.6? d) was rated A and scored below 96.8? e) was rated B given scored below 78.9? f) scored above 78.9 given rated A