# Thread: Some values of z

1. ## Some values of z

The WAIS is the most common IQ test. The scale of scores is approximately Normal with mean 100 and standard deviation 15.

People with WAIS scores below 70 are considered mentally retarded when, for example, applying for Social Security disability benefits.

What percent of adults are retarded by this criterion?

i know $\displaystyle z = \frac{x-\mu}{\sigma}$

I am just not sure how to find this percent its asking for with only the given info.

Any help to get me started would be greatly appreciated

Thank you

2. $\displaystyle \displaystyle P\left(Z< \frac{x-\mu}{\sigma} \right) = P\left(Z< \frac{70-100}{15} \right) = P(Z< -2) = \frac{0.05}{2}$

3. Can i ask what the P stands for? i have never seen that before.. Thank you pickslides

4. Also i get how you got Z < -2 but can you explain where the $\displaystyle \frac{0.05}{2}$ comes from?

For my final answer i am getting 0.0228 or 2.28% from looking at the table in my book for area under the curve to the left of the Z value -2.

5. P stands for probabilty and 95% of values lie between 2 standard deviations of the mean.

The differences in our results are negligable.