Question

he average student loan debt for college graduates is $25,900. Suppose that that distribution is normal and that the standard deviation is $10,200. 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. Find the probability that the college graduate has between $14,950 and $28,050 in student loan debt.

Answer 1

Given that the average student loan debt is $25,900.

`\mu=25,900`

The standard deviation is $10,200.

`\sigma=10,200`

Let X be the student loan debt of a randomly selected college graduate.

`Z=(x-\mu)/(\sigma)`

When x =$14,950, we have;

`\begin{gathered} Z_1=(14950-25900)/(10200) \\ Z_1=-1.0735 \end{gathered}`

When x=$28,050, we have;

`\begin{gathered} Z_2=(28050-25900)/(10200) \\ Z_2=0.2108 \end{gathered}`

Then,

[tex]\begin{gathered} P(-1.0735

The probability that the college graduate has between $14,950 and $28,050 in student loan debt is 0.4420