Question

Western lowland gorillas, whose main habitat is in central Africa, have a mean weight of $275$pounds with a standard deviation of $40$pounds. Capuchin monkeys, whose main habitat is Brazil and other parts of Latin America, have a mean weight of $6$pounds with a standard deviation of $1.1$pounds. Both distributions of weight are approximately Normally distributed. If a particular western lowland gorilla is known to weigh $345$pounds, approximately how much would a capuchin monkey have to weigh, in pounds, to have the same standardized weight as the gorilla?

a. $4.08$

b. $7.27$

c. $7.93$

d.$8.20$

e. There is not enough information to determine the weight of a capuchin monkey.

Short answer

The correct answer is option (c)$7.93.$

Step-by-step solution

Given information

For the gorilla

$$\begin{gathered} \mu =275 \\ \sigma =40 \end{gathered}$$

For capuchin monkey

$$\begin{gathered} \mu =6 \\ \sigma =1.1 \end{gathered}$$

Explanation

The average weight of western lowland gorillas and capuchin monkeys is given in the question, and both weight distributions are nearly normal. First, determine the gorilla's $z-$score, i.e.

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

The capuchin monkey's $z-$score is now also $1.75$. Because their weights are $1.75$standard deviations from their respective averages, their$z-$scores must be identical to have the same standardised weight. As a result, we'll solve for the capuchin monkey as follows:

From the given data

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

Option (c) is correct.