Chapter 3.2, Problem 3.34E

To determine

To find the score that represents the scores in top 25%.

Answer to Problem 3.34E

The value that shows the above 25% of the data value is 126.8625.

Explanation of Solution

Given:

  $x~\text{N(110, 25)}$

Calculation:

  $\begin{array}{l}P\left(Z>x\right)=0.25\\ \Rightarrow P\left(Z>\frac{x-110}{25}\right)=0.25\\ \Rightarrow \frac{x-110}{25}=0.6745\\ \Rightarrow x=0.6745\times 25+110\\ \Rightarrow 126.8625\end{array}$