# z-score question

• Jan 27th 2009, 03:09 PM
perron
z-score question
A university aacepts only applicats scoring in the top 16% on an entrance exam. Each year the test scores are normaly distributed with a standard deviation of 30. What is the highest value that the mean can have for Fred to be accepted with a score of 520?

I was able to figure out the answer to this question but now I can't seem to figure out how I got the z-score number of -0.99????

z=-0.99
x=520
o=30

mean= x+ (z+o)
= 520+(-0.99 x 30)
=490.3

ahh, help.
• Jan 27th 2009, 05:36 PM
Chris L T521
Quote:

Originally Posted by perron
A university aacepts only applicats scoring in the top 16% on an entrance exam. Each year the test scores are normaly distributed with a standard deviation of 30. What is the highest value that the mean can have for Fred to be accepted with a score of 520?

I was able to figure out the answer to this question but now I can't seem to figure out how I got the z-score number of -0.99????

z=-0.99
x=520
o=30

mean= x+ (z+o)
= 520+(-0.99 x 30)
=490.3

ahh, help.

Note that he needs to be in the top 16% or the 84th percentile.

Thus, it can be seen in tables, that the z-score that corresponds to the 84th percentile would be .994. (If you have a TI-83, you can find this z value by inputting invNorm(.84))

Since $x=520$ and $\sigma = 30$, we see that $\frac{520-\mu}{30}=.994$, which leads to something close to your result. I end up with $\mu=490.18$

Does this clarify things?