Question

The average student loan debt for college graduates is $25,500. Suppose that that distribution is normal and that the standard deviation is $12,000. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar.

The middle 20% of college graduates' loan debt lies between what two numbers?

Low: $

High: $

Answer 1

Given that,

mean = $\mu$ = $25500

standard deviation = $\sigma$ = $12000

middle 20 % of score is

P(-z < Z < z) = 0.20

P(Z < z) - P(Z < -z) = 0.20

2 P(Z < z) - 1 = 0.20

2 P(Z < z) = 1 + 0.20= 1.20

P(Z < z) = 1.20 / 2 = 0.6

P(Z < 0.25) = 0.6

z  ±0.25

Using z-score formula  

x= z * $\sigma$ + $\mu$

x= - 0.25 *12000+25500

x= 22500

Using z-score formula  

x= z * $\sigma$ + $\mu$

x= 0.25 *12000+25500

x= 28500

Low: $22500

High: $28500