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 (%) (ii) The original default rate on the sample of 40,000 card holders was extremely high.
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 (%) (ii) The original default rate on the sample of 40,000 card holders was extremely high.
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 (%) (ii) The original default rate on the sample of 40,000 card holders was extremely high.
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 (%)
(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.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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