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 100. (a) Find the credit score that defines the upper 5 percent. (Use Excel or Appendix C to calculate the z-value. Round your final answer to 2 decimal places.) Credit score (b) Seventy-five percent of the customers will have a credit score higher than what value? (Use Excel or Appendix C to calculate the z-value. Round your final answer to 2 decimal places.) Credit score (c) Within what range would the middle 80 percent of credit scores lie? (Use Excel or Appendix C to calculate the z-value. Round your final answer to 2 decimal places.) Range to

a) The credit score that defines the upper 5% is 764.50.

b) Seventy-five percent of the customers will have a credit score higher than 532.5.

c)  Range 472 to 728.

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

a) Find the credit score that defines the upper 5 percent.

Value of X when Z has a pvalue of 1-0.05 = 0.95. So X when Z = 1.645.

The credit score that defines the upper 5% is 764.50.

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

100 - 75 = 25

This the 25th percentile, which is the value of X when Z has a pvalue of 0.25. So it ix X when Z = -0.675.

Seventy-five percent of the customers will have a credit score higher than 532.5.

(c) Within what range would the middle 80 percent of credit scores lie?

50 - 80/2 = 10th percentile to 50 + 80/2 = 90th percentile.

10th percentile

value of X when Z has a pvalue of 0.1. So X when Z = -1.28.

90th percentile

Range 472 to 728.

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743

a

step-by-step explanation:

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