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According to the Institute for College Access and Success, the mean student loan debt of students who graduated from college in 2013 was $28,400. Assume that the standard deviation was $30,000.
You want to know if the mean is the same in Wisconsin as in the US as a whole, so you survey a random sample of 100 people who graduated from Wisconsin colleges in 2013. You record the loan amount of each person; if they have no loans, then you record $0. You find that the mean amount of student loan debt in your survey was $22,658.
Assuming that the average student loan debt is the same in Wisconsin as in the whole US, what is the probability that the average in your sample would be $22,658 or less?
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