# Thread: [SOLVED] Average credit score

1. ## [SOLVED] Average credit score

At a bank, average credit score of a 35 yr old is normally distributed with a mean of 600 and std dev of 100.

a. score for top 5%
b. 75% of applicants will have at least what score?
c. Between what two credit scores will 80% of the applicants fall if the applicants are symmetrically distributed?

doesn't this problem involve finding the z score? but 5-600/100 = a number outside the chart

2. Originally Posted by Famas
At a bank, average credit score of a 35 yr old is normally distributed with a mean of 600 and std dev of 100.

a. score for top 5%
b. 75% of applicants will have at least what score?
c. Between what two credit scores will 80% of the applicants fall if the applicants are symmetrically distributed?

doesn't this problem involve finding the z score? but 5-600/100 = a number outside the chart
a. $\displaystyle Z = \frac{X - 600}{100}$

You want the value of $\displaystyle \alpha$ such that $\displaystyle \Pr(X > \alpha) = 0.05$.

Note that $\displaystyle Pr(Z > 1.64485) = 0.05$.

Therefore $\displaystyle 1.64485 = \frac{\alpha - 600}{100} \Rightarrow \alpha = ....$

b. Do similarly to a.

c. You want the value of $\displaystyle \beta$ such that $\displaystyle \Pr(X > \beta) = 0.1$. Draw a simple curve and you'll see this. Now do similarly to a.

The lower and upper credit scores are then $\displaystyle 600 - (\beta - 600) = 1200 - \beta\,$ and $\displaystyle \, \beta$.