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 600 and a standard deviation of 70.

(a) 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.)

(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.)

(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.)

Explanation / Answer

mean is 600 and s is 70

a) For upper 20% we need to look at the value of z at 80% from left of curve from normal distribution table, which is z= 0.85

thus answer is 600+0.85*70=659.5

b) for bottom 15% the z value for 85% from normal table can be negated. thus it is -1.04

thus answer is 600-1.04*70=527.2

c) for middle 90%, the z value for lower bound is given as -1.65 and for upper bound it is 1.65

thus lower bound is 600-1.65*70=484.5

the upper bound is 600+1.65*70=715.5

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