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 125. (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.) Credit score (b) Eighty-five percent of the customers will have a credit score higher than what value

a) The credit score that defines the upper 20% is 705.

b) Eighty-five percent of the customers will have a credit score higher than 470.38.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of 600 and a standard deviation of 125.

This means that

(a) Find the credit score that defines the upper 20 percent.

This is the 100 - 20 = 80th percetile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84.

The credit score that defines the upper 20% is 705.

(b) Eighty-five percent of the customers will have a credit score higher than what value?

This is the 100 - 85 = 15th percentile, which is X when Z has a pvalue of 0.15. So X when Z = -1.037.

Eighty-five percent of the customers will have a credit score higher than 470.38.

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