Question

The average student loan debt for college graduates is $25,300. Suppose that that distribution is normal and that the standard deviation is $14,700. 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.

a. What is the distribution of X? X ~ N(,)

b Find the probability that the college graduate has between $7,950 and $25,200 in student loan debt.

c. The middle 10% of college graduates' loan debt lies between what two numbers?
     Low: $
     High: $

Answer 1

Solution:- Given that mean = 25300, sd = 14700

a. The distribution of X ~ N(25300 , 14700)

b. P(7950 < X < 25200) = P((7950-25300)/14700 < (X-mean)/sd < (25200-25300)/14700)
= P(-1.1803 < Z < -0.0068)
= P(Z < −0.0068) − P(Z < −1.1803)
= 0.4960 - 0.1190
= 0.3770

P(Z < 0.0068) can be found by using the following standard normal table :

P(Z < 1.1803) can be found by using the following standard normal table :

c. for Z = +/- 1.645

Low : X - Z*s = 25300 - 1.645*14700 = $1118.5

high : X + Z*s = 25300 + 1.645*14700 = $49481.5