Question

Many students accumulate debt by the time they graduate from college. Shown in the following table is the percentage of graduates with debt and the average amount of debt for these graduates at four universities and four liberal arts colleges. University % with Debt Amount($) College % with Debt Amount($)

1 71 32,950 1 81 28,751

2 68 32,140 2 93 24,000

3 51 11,226 3 52 10,209

4 64 11,858 4 49 11,018

a. If you randomly choose a graduate of College 2, what is the probability that this individual graduated with debt (to 2 decimals)?

b. If you randomly choose one of these eight institutions for a follow-up study on student loans, what is the probability that you will choose an institution with more than 60% of its graduates having debt (to 3 decimals)?

c. If you randomly choose one of these eight institutions for a follow-up study on student loans, what is the probability that you will choose an institution whose graduates with debts have an average debt of more than $ 24,000 (to 3 decimals)?

d. What is the probability that a graduate of University 1 does not have debt (to 2 decimals)?

e. For graduates of University 1 with debt, the average amount of debt is $ 32,950. Considering all graduates from University 1, what is the average debt per graduate? Round to nearest dollar. $

Answer 1

Solution:

a)

probability that this individual graduated with debt given from graduate of College 2 =0.93

b)

probability that you will choose an institution with more than 90% of its graduates having debt = 5/8

= 0.625

(as there is 5 institutes college 1,2 and 4 out of 8 with more than 60% of its graduates having debt )

c)

probability that you will choose an institution whose graduates with debts have an average debt of more than $ 24000 = 3/8 =0.375(3 such institute ; university 1 and 2 out of 8)

d)

probability that a graduate of University 1 does not have debt =1-0.71=0.29

e) average debt per graduate =0.71*32950 =23394.5~ $23395