Question

Average student loan debt is $25850, with normal distribution and std deviation is $10,700. The middle 20%of loan debt lies between what two numbers?

Answer 1

Solution:

Given, the Normal distribution with,

   = 25850

= 10700

Consider that the middle 20%of loan debt lies between a and b.

P(a < X < b ) = 0.20

Since the normal distribution is symmetric and bell shaped .,

P(X < a) = 0.40 and P(X > b) = 0.40

So ,

P(X < a) = 0.40 and P(X < b) = 0.60

But from z table ,

P(Z < -0.2533) = 0.40 and P(Z < 0.2533 ) = 0.60

-z = -0.2533 and z = 0.2533

Using z score formula ,

a = + (-z * ) = 25850 + (-0.2533 * 10700) = 23139.69 = 23140

b = + (-z * ) = 25850 + (0.2533 * 10700) = 28560.31 = 28560

Answer : The middle 20%of loan debt lies between 23140 and 28560