Chapter 3.2, Problem 3.46E

To determine

To find: the IQ score was at 98^th percentile.

Answer to Problem 3.46E

130.75

Explanation of Solution

Given:

98^th percentile =98%

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

Formula used:

  $z=\frac{x-\mu }{\sigma }$

Calculation:

Z-score corresponding to 98% = 0.98

z=2.05

  $\begin{array}{c}z=\frac{x-\mu }{\sigma }\\ 2.05=\frac{x-100}{15}\\ 30.75=x-100\\ x=130.75\end{array}$

The score is 130.75 or about 131