Chapter 8.1, Problem 8.18E

To determine

To calculate how high must a person score on the WAIS test to be in the top $10\%$ of all scores using table A or calculator.

Answer to Problem 8.18E

The top $10\%$ has a WAIS score of at least $119.2$ .

Explanation of Solution

Given:

  $\begin{array}{l}\mu =100\\ \sigma =15\end{array}$

The top $10\%$ has the cutoff with the property that $10\%$ of the values lie above it and thus $90\%$ of the values lie below it.

Determine the z -scores in the probability table that corresponds with a probability of $90\%$ .

  $z=1.28$

The standardized score is as:

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ x=\mu +2\sigma \\ x=100+1.28(15)=119.2\end{array}$

We then note that the top $10\%$ has a WAIS score of at least $119.2$ .