Chapter 12, Problem AP4.24CPT

To determine

To find out approximately how much would a capuchin monkey have to weigh in pounds to have the same standardized weight as the gorilla.

Answer to Problem AP4.24CPT

Option (c) is the correct option.

Explanation of Solution

In the question, western lowland gorillas and the capuchin monkeys average weight are given and both the distributions of weight are approximately normal. Let us first find the z-score of the gorilla, i.e.

  $\begin{array}{l}z=\frac{345-275}{40}\\ =1.75\end{array}$

As for gorilla,

  $\begin{array}{l}\mu =275\\ \sigma =40\end{array}$

Now the z-score of the capuchin monkey is also be $1.75$ . Their z-scores must be equivalent to have the same standardized weight because both their weights will be $1.75$ standard deviations from their respective means. Thus, we will solve for the capuchin monkey as:

Given for capuchin monkey that,

  $\begin{array}{l}\mu =6\\ \sigma =1.1\end{array}$

Thus, we have,

  $\begin{array}{l}1.75=\frac{x-6}{1.1}\\ \Rightarrow 1.925=x-6\\ \Rightarrow x=7.925\approx 7.93\end{array}$

Thus, option (c) is the correct option.