Question

A charity provides loans of $6,000 for students to attend a one year vocational business college. Upon graduation students repay 10% of their first year salary back to the charity. First year salaries are Normally distributed with a mean of $50,000 and a standard deviation of $12,000.

Some students complain that they are repaying over 25% more than they borrowed. What is the probability that a student is in this position?

Answer 1

Let X be the first-year salaries.

We are given the following information:

X ~ Normal(50000,12000)

We need to find the probability that students are paying over 25% more than they borrowed i.e. 6000(1+.25) = 7500. Since they are paying 10% of their salary that would effectively make their salary 75000.

i..e we need to find the following probability that their salaries are greater than 75000 i.e.

.

The corresponding z-value needed to be computed is:

Therefore, we get that

The following is obtained graphically:4

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