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The accounts of 4,500 credit card customers out of a sample of 40,000 that were reviewed did not perform satisfactorily. The credit scores assigned to these applicants when originally assessed had a mean of 70 and standard deviation of 8. The scores of the remaining customers had a mean of 87 and a standard deviation of 12. Assuming these distributions are approximately normal, if the cut-off score was revised upward to 82.
(i) Complete the following table:
Creditworthiness
High
Low
Mean credit score
87
70
Standard deviation of credit score
12
8
Probability of receiving credit (%)
Probability of being denied credit (%)
(ii) The original default rate on the sample of 40,000 card holders was extremely high. What impact would be setting the cut-off at 82 have on the default rate? Show calculations. Is this adjustment reasonable? Discuss.
(iii)Based on the credit evaluation process. Complete the following table and identify the Type I and Type II errors. All quadrants need to be identified.
Analyzed credit quality
Actual credit quality
Good
Bad
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