The credit scores of 35yearolds applying for a mortgage at U

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.

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.)

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.)

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.)

Solution

a)
Normal Distribution
Mean ( u ) =600
Standard Deviation ( sd )=70
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z < x ) = 0.8
Value of z to the cumulative probability of 0.8 from normal table is 0.842
P( x-u/s.d < x - 600/70 ) = 0.8
That is, ( x - 600/70 ) = 0.84
--> x = 0.84 * 70 + 600 = 658.94                  

b)              
P ( Z > x ) = 0.85
Value of z to the cumulative probability of 0.85 from normal table is -1.04
P( x-u/ (s.d) > x - 600/70) = 0.85
That is, ( x - 600/70) = -1.04
--> x = -1.04 * 70+600 = 527.48