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The question is:

**An estimated 1.8 million students take on student loans to pay ever-rising tuition and room and board (New York Times, April 17, 2009). It is also known that the average cumulative debt of recent college graduates is about $22,500.

The cumulative debt for college graduates is normally distributed with a standard deviation of $7,000.

Approximately how many recent college graduates have accumulated a student loan of more than $30,000?**

What I've done: 30,000-22500/7000=1.071428571 I then looked this up on the z table but that wouldn't give me the correct answer. What exactly am I doing wrong?

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  • $\begingroup$ What number did you get? $\endgroup$ – André Nicolas Oct 26 '13 at 16:18
  • $\begingroup$ I got .8577 from the z-table $\endgroup$ – Kim Oct 26 '13 at 16:20
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    $\begingroup$ Then do $(1800000)(1-0.8577)$. If it is clear why, good. If not, I can give some detail about why. $\endgroup$ – André Nicolas Oct 26 '13 at 16:22
  • $\begingroup$ Thanks,I believe I do need details as to why this is the answer. $\endgroup$ – Kim Oct 26 '13 at 16:51
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Under the stated assumptions, you calculated correctly the probability that a student has debt less than or equal to $30000$. This probability is approximately $0.8577$.

So the probability that the debt is greater than $30000$ is approximately $1-0.8577$, which is $0.1423$.

You were asked to estimate the number of recent college graduates with level of debt $\gt 30000$. You are probably expected to assume that the $1.8$ million counts these, though the wording does not fully support this. But if we assume that there are indeed $1.8$ million in the recent college graduate category, then the number of these with debt $\gt 30000$ should be approximately $(1800000)(0.1423)$.

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    $\begingroup$ You are welcome. $\endgroup$ – André Nicolas Oct 26 '13 at 18:28
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Debt of more than 30000. So the area you should be looking for is $$ 1- \Phi(\frac{30000-22500}{7000})$$

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