Chapter 3.2, Problem 3.36E

(a)

To determine

To find the score that represents the score that represent the 85^th percentile for males.

Answer to Problem 3.36E

The value that shows the 85^th percentile is 655.2952.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Females ~N(500, 111)}\\ \text{Males ~N(533,118)}\end{array}$

Calculation:

  $\begin{array}{l}P\left(X<x\right)=0.85\\ \Rightarrow P\left(z<\frac{x-533}{118}\right)=0.85\\ \Rightarrow \frac{x-533}{118}=1.0364\\ \Rightarrow x=1.0364\times 118+533\\ \Rightarrow x=655.2952\end{array}$

(b)

To determine

To find the score that represents the score that represent the 85^th percentile for females.

Answer to Problem 3.36E

The value that shows the 85^th percentile is 615.0404.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Females ~N(500, 111)}\\ \text{Males ~N(533,118)}\end{array}$

Calculation:

  $\begin{array}{l}P\left(X<x\right)=0.85\\ \Rightarrow P\left(z<\frac{x-500}{111}\right)=0.85\\ \Rightarrow \frac{x-500}{111}=1.0364\\ \Rightarrow x=1.0364\times 111+500\\ \Rightarrow x=615.0404\end{array}$