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 620 and a standard deviation of 90. Find the credit score that defines the upper 20 percent. (Use Excel or Appendix C to calculate the z-value. Round your final answer to 2 decimal places.) Credit score 735.34 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 526.72 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 471.95 to 768.05

Explanation / Answer

Mean M= 620

Standard deviation sd = 90

Z= (X-M)/sd

P(Z) can be obtained from normal distribution table

A) upper 20% is the value corresponding to the lower 80%

So, P(Z) = 0.8

Z= 0.84

(X - 620)/90 = 0.84

So, X = 695.6

B) P(Z) = 1-0.85 = 0.15

Z= -1.036

(X-620)/90 = -1.036

So, X = 497.6

C) Middle 90% lies between P(Z)=0.05 and Z= 0.95

Z corresponding to P(z) = 0.05 is -1.645

(X-620)/90 = -1.645

X= 471.91

Z value corresponding to P(z)= 0.95 is 1.645

(x-620)/90=1.645

So x = 768.05

So, the range = 471.95 to 768.05

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