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 670 and a standard deviation of 125.

(a) Find the credit score that defines the upper 15 percent. (Use Excel or Appendix C to calculate the z-value. Round your final answer to 2 decimal places.)

Credit score            

(b) Fifty-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 60 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 PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 670
standard Deviation ( sd )= 125
a.the credit score that defines the upper 15 percent
P ( Z > x ) = 0.15
Value of z to the cumulative probability of 0.15 from normal table is 1.04
P( x-u / (s.d) > x - 670/125) = 0.15
That is, ( x - 670/125) = 1.04
--> x = 1.04 * 125+670 = 799.55
b. Fifty-five percent of the customers will have a credit score higher than what value
P ( Z > x ) = 0.55
Value of z to the cumulative probability of 0.55 from normal table is -0.13
P( x-u / (s.d) > x - 670/125) = 0.55
That is, ( x - 670/125) = -0.13
--> x = -0.13 * 125+670 = 654.29
c.the middle 60 percent of credit scores lie
P ( Z > x ) = 0.6
Value of z to the cumulative probability of 0.6 from normal table is -0.25
P( x-u / (s.d) > x - 670/125) = 0.6
That is, ( x - 670/125) = -0.25
--> x = -0.25 * 125+670 = 638.33
P ( Z < x ) = 0.6
Value of z to the cumulative probability of 0.6 from normal table is 0.25
P( x-u/s.d < x - 670/125 ) = 0.6
That is, ( x - 670/125 ) = 0.25
--> x = 0.25 * 125 + 670 = 701.67
range in the middle of 60% = 710.67-638.33 = 72.34

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