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Chapter 12: Q. AP4.24 (page 831)

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

Expert verified

The correct answer is option (c)7.93.

Step by step solution

01

Given information

For the gorilla

μ=275σ=40

For capuchin monkey

μ=6σ=1.1

02

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.

z=345-27540=1.75

The capuchin monkey's z-score is now also 1.75. Because their weights are 1.75standard deviations from their respective averages, theirz-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

1.75=x-61.11.925=x-6x=7.925≈7.93

Option (c) is correct.

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