# Help needed…Statistics probability and z table…stuck

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 $30,000?** What I've done: 30,000-22500/7000=1.071428571 I then looked this up on the z table but that wouldn't give me the correct answer. What exactly am I doing wrong? • What number did you get? – André Nicolas Oct 26 '13 at 16:18 • I got .8577 from the z-table – Kim Oct 26 '13 at 16:20 • Then do$(1800000)(1-0.8577)$. If it is clear why, good. If not, I can give some detail about why. – André Nicolas Oct 26 '13 at 16:22 • Thanks,I believe I do need details as to why this is the answer. – Kim Oct 26 '13 at 16:51 ## 2 Answers 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)\$.

• You are welcome. – André Nicolas Oct 26 '13 at 18:28

Debt of more than 30000. So the area you should be looking for is $$1- \Phi(\frac{30000-22500}{7000})$$