QUESTION 3(b) The accounts of 4,500 credit card customers out of a sample of 40,000 that were
Question:
QUESTION 3(b)
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.
- 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 (%) |
QUESTION 3(b)(continued)
(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.
Analysed credit quality | Actual credit quality | |
Good | Bad | |
Good | ||
Bad |