Discussion Question 2: Approve or Not-approve Suppose that a bank uses an applicant's score on some criteria to decide whether or not to approve a loan for the applicant. Suppose for now that these scores follow normal distributions, both for people who would repay to the loan and for those who would not. Those who would repay the loan have a mean of 70 and standard deviation of 8; those who would not repay the loan have a mean of 30 and standard deviation of 8. Please only answer one part at a time and don't skip part. If we sketch both distributions in the same coordinate system, it looks like the following: 1 1 I 61" 'i" The left one is the distribution for those who would not repay the loan and the right one is the distribution for those who would repay the loan. (1) Suggest a decision rule, based on using an applicant's score, for deciding whether or not to give a loan to the applicant. Describe the two kinds of classication errors that could be made in this situation. (2) Determine the probabilities of the two kinds of error with this rule. Write a sentence or two to interpret the two error probabilities in context. Now suppose that the credit scores are normally distributed with mean 60 and standard deviation 8 among those who would repay the loan, as compared to mean 41] and standard deviation 12 among those who would not repay the loan. The distributions look like the following: 1 1 1 1 I (3) Describe how this scenario differs from the previous one. (4) Determine the probabilities of the two kinds of error (using the decision rule based on a cut-off value of 50). Write a sentence or two to interpret the two error probabilities in context. (5) In which direction smaller or larger would you need to change the decision rule 's cutoff value in order to decrease the probability that an applicant who would repay the loan is denied? ACTIVITIES AND ASSIGNMENTS FOR WEEK 5 3 (6) How would the probability of the other kind of error approving a loan for an applicant who would not repay it change with this new cutoff value (as described in the last part)? (7) Determine the cutoff value needed to decrease the error probability in Part (5) to .05. Does this conrm your answer to Part (5)? (8) Determine the other error probability with this new cut-off rule. Does this conrm your answer to Part (6)? (9) Write a sentence or two to interpret the two error probabilities in context. (10) Repeat Part (7) to (9) with the goal of decreasing the probability that an applicant who would not repay the loan is approved to 0.05. (11) If you consider the two kinds of errors to be equally serious, how might you decide which of the three decision rules considered thus far is the best? (12) Calculate the average of the two error probabilities for the following three cutoff values: 50, 46.84 and 59.74. (13) Which cutoff value from the above is the best, according to this criterion, among these three options? (14) Do you have other suggestions about cutoff value that we should use that you think will work better