The credit scores of 35-year-olds applying for a mortgage at Ulysses Mortgage As

Question

The credit scores of 35-year-olds applying for a mortgage at Ulysses Mortgage Associates are normally distributed with a mean of 610 and a standard deviation of 90. (a) Find the credit score that defines the upper 10 percent. (Use Excel or Appendix C to calculate the z-value. Round your final answer to 2 decimal places.) Credit score (b) Sixty-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 70 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

Explanation / Answer

The credit scores of 35-year-olds applying for a mortgage at Ulysses Mortgage Associates are normally distributed with a mean of 610 and a standard deviation of 90.

a. Find the credit score that defines the upper 10 percent.

Find the credit score that defines the upper 10%

The z-score for 90% probability can be calculated as NORM.S.INV(0.90)= 1.2816 (by using excel)

Credit score = z *SD +X

Where,

Mean X = 610

Standard deviation, SD = 90

Therefore

Credit score = 1.2816 *90 + 610

=115.34 +610

=725.34

b. Sixty-five percent of the customers will have a credit score higher than what value?

The left-tail cutoff will be 35%

And z-score can be calculated as NORM.S.INV(0.35)= -0.3853 (by using excel)

Now credit score = z *SD +X

= -0.3853*90 + 610

= -34.68 +610

= 575.32

c. Within what range would the middle 70 percent of credit scores lie?

The credit scores will lie between a left-tail cutoff at 15% and a right-tail cutoff at 85%

z = NORM.S.INV(0.15)= -1.0364 and z=NORM.S.INV(0.85) = +1.0364

Lower range = z *SD +X

= -1.0364*90 + 610

= -93.2790 +610

= 516.72

And Upper range = z *SD +X

= 1.0364*90 + 610

= 93.2790 +610

= 703.28

Therefore the middle 70 percent of credit scores lie between 516.72 - 703.28

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