Z-Scores: beyond what scores do most extreme 5% lie?

Hey,

I've been working on a homework assignment regarding z-scores with an IQ test which has a mean of 100 and a standard deviation of 16. Xbar=100, S=16

I have my super handy table for areas under the normal curve.

I found the 2 scores which fall between the central 20% of the population, which are 95 and 106.
Using the table, I got these scores using x=xbar+(area beyond z statistic in table)(standard deviation) [so 100+(.3446)(16)] for the upper score.

The next questions is: beyond what scores do the most extreme 5% of the distribution lie? I imagine they're talking about the two end of the tails, but I don't know exactly how to go about doing this. Would someone help out?

Re: Z-Score action

For the most extreme 5%, we want the scores below 5% and the scores above 95%.

Look up .05 and .95 in the body of the table and find their corresponding z-scores.

Plug them into the z-score formula and solve for x.

\(\displaystyle z=\frac{x-{\mu}}{\sigma}\)

Re: Z-Score action

You sure it's not 2.5% on each end?

Re: Z-Score action

Yes, because they asked for the lower and upper 5%.

Re: Z-Score action

Awesome, thanks!

Re: Z-Score action

One more question regarding another problem.

In separate classes and separate exams, Fred gets 39(mean 43, Standard Dev 5.5) and Sue gets 32 (mean 31, s 3.1)

The questions are who did better? and by how much?

I calculate the z-scores (-.73, -2.9) but can someone help me figure out their percentiles. I'm pretty sure i need to get the data from a statistical table I have access to (the one with z score, area between z and mean, and area beyond z) though I'm not sure from which columns I retrieve the data from, or if I need to do any figuring. Thanks