According to Student Monitor, a New Jersey research firm, the average cumulated college 10
student loan debt for a graduating senior is $25,760. Assume that the standard deviation of
such student loan debt is $5,684. Thirty percent of these graduating seniors owe more than
what amount? What is the probability that graduating seniors owe less than $24,700 loan?
Answers
Given : average student loan debt for a graduating senior is $25,760.
standard deviation of such student loan debt is $5,684.
To Find : 30 % of these graduating seniors owe more than what amount?
What is the probability that graduating seniors owe less than $24,700 loan?
Solution:
Mean = $25,760
standard deviation = $5,684
Z score = ( Value - Mean)/SD
30% of these graduating seniors owe more than amount =A
=> 70 % of these graduating seniors owe less than Amount A
Z score for 70% = 0.525
0.525 = (A - 25,760)/5,684
=> A = 28,744.1 $
30% of these graduating seniors owe more than amount 28,744 $
probability that graduating seniors owe less than $24,700 loan
Z score == (24,700 - 25,760)/ 5,684 = -0.186 = 0.427
0.427 is the probability that graduating seniors owe less than $24,700 loan
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