On a peer-to-peer (P2P) lending website, borrowers complete a approval scoring form that lenders use to assess creditworthiness. Borrowers are rated A, B, C or D, based on their scores, with A having the highest scores and D having the lowest.

In a large sample of borrowers, 9% were rated A, 35% were rated B, 25% were rated C, and the rest were rated D. Suppose the scores are normally distributed with a mean of 348 and a standard deviation of 38.

a) What is the cut-off score between A and B?

b) What is the cut-off score between B and C?

c) What is the cut-off score between C and D?

d) What score corresponds to the 25th percentile?

e) What score corresponds to the 75th percentile?

f) What is the minimum score above which lies 13% of the scores?

g) Between what scores will the middle 92% of scores lie?

Lower value =

Higher value =

h) What rating will a score of 411 receive?Select an answer

C-rating

B-rating

A-rating

i) What rating will a score of 338 receive?Select an answer

D-rating

C-rating

B-rating

A-rating