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Chapter 12: Q. 24 (page 803)

Western lowland gorillas, whose main habitat is the central African continent, have a mean weight of 275poundswith a standard deviation of 40pounds. Capuchin monkeys, whose main habitat is Brazil and a few other parts of Latin America, have a mean weight of 6poundswith a standard deviation of 1.1pounds. Both weight distributions 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 lowland 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

As the weight of a capuchin monkey is,x鈮�7.93

So, (c) option is the correct one.

Step by step solution

01

Given information

Mean weight of western lowland gorillas is, a=275pounds

And its standard deviation is, S.D1=40pounds

And its weight is,w=345pounds

Mean weight of Capuchin monkeys is, b=6pounds

And its standard deviation is,S.D2=1.1pounds

02

Simplify

We know that,

The z-score of gorilla is given as,

z=w-aS.D1=345-27540=1.75

As the standardized weight of capuchin monkey is same as that of gorilla. So, their z-scores must be equal to each other i.e. z-score of capuchin monkey is, z=1.75

Now, as we know z- score is given as,

z=x-bS.D2=1.75x-61.1=1.75x-6=1.75脳1.1x-6=1.925x=7.925鈮�7.93

Therefore, from above we get the correct option i.e. (c)

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