The Credit Scores Of 35-Year-Olds Applying For A Mortgage

The Credit Scores Of 35 Year Olds Applying For A Mortgage At Ulysses M

The credit scores of 35-year-olds applying for a mortgage at Ulysses Mortgage Associates are normally distributed with a mean of 620 and a standard deviation of 90. (a) Find the credit score that defines the upper 20 percent. (Use Excel or Appendix C for calculation of z-value. Round your final answer to 2 decimal places.) Credit score (b) Eighty-five percent of the customers will have a credit score higher than what value? (Use Excel or Appendix C for calculation of z-value. Round your final answer to 2 decimal places.) Credit score (c) Within what range would the middle 90 percent of credit scores lie? (Use Excel or Appendix C for calculation of z-value. Round your final answer to 2 decimal places.) Range to

Paper For Above instruction

This paper addresses the statistical analysis of credit scores among 35-year-olds applying for mortgages at Ulysses Mortgage Associates. These scores follow a normal distribution characterized by a mean of 620 and a standard deviation of 90. The analysis involves identifying specific percentile scores within this distribution, which are valuable for understanding creditworthiness and risk assessment in the mortgage lending process.

Part (a): Determining the Credit Score that Defines the Upper 20 Percent

The first task is to find the credit score that marks the threshold below which 80% of the applicants' scores fall, effectively the 80th percentile of the distribution. Using the standard normal distribution table or Excel, we need to find the z-value corresponding to the 80th percentile. According to Excel's NORM.S.INV(0.80), the z-score is approximately 0.84.

Applying the z-score formula:

Score = Mean + (z * Standard Deviation)


Score = 620 + (0.84 * 90) = 620 + 75.6 = 695.60

Thus, the credit score that defines the upper 20 percent is approximately 695.60.

Part (b): Credit Score Above Which 85% of Customers Fall

Next, we find the score above which 85% of customers have scores. This corresponds to the 15th percentile because 100% - 85% = 15%. Using Excel's NORM.S.INV(0.15), the z-value is approximately -1.04.

Applying the z-score formula:

Score = 620 + (-1.04 * 90) = 620 - 93.6 = 526.40

Therefore, approximately 526.40 is the credit score above which 85% of customers will have scores.

Part (c): Range for the Middle 90% of Credit Scores

Finally, to find the range covering the middle 90%, we determine the scores at the 5th and 95th percentiles, because 5% lies in each tail outside the middle 90%.

- The z-value for the 5th percentile is approximately -1.64 (NORM.S.INV(0.05))

- The z-value for the 95th percentile is approximately 1.64 (NORM.S.INV(0.95))

Calculating the lower bound:

Lower bound = 620 + (-1.64 * 90) = 620 - 147.6 = 472.40

Calculating the upper bound:

Upper bound = 620 + (1.64 * 90) = 620 + 147.6 = 767.60

Hence, the middle 90% of credit scores lie within the range 472.40 to 767.60.

References

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  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics. W.H. Freeman.
  • Ulysses Mortgage Associates (Data Source). (2023). Internal Data Records.
  • Excel Documentation. (2023). Microsoft Support. https://support.microsoft.com
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