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Question 13 of 30

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M:C:MC:9

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SAT

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PSAT/NMSQT

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PSAT 10

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Problem Solving and Data Analysis

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At a primate reserve, the mean age of all the male primates is 15 years, and the mean age of all female primates is 19 years. Which of the following must be true about the mean age m of the combined group of male and female primates at the primate reserve?

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m equals 17

Correct Answer: 
No

m greater than 17

Correct Answer: 
No

m less than 17

Correct Answer: 
No

15 less than m less than 19

Correct Answer: 
Yes

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Choice D is correct. The student must reason that because the mean of the males is lower than that of the females, the combined mean cannot be greater than or equal to that of the females, while also reasoning that because the mean of the females is greater than that of the males, the combined mean cannot be less than or equal to the mean of the males. Therefore the combined mean must be between the two separate means.

Choice A is not the correct answer. This answer results from a student finding the mean of the two means. This answer makes an unjustified assumption that there are an equal number of male and female primates.

Choice B is not the correct answer. This answer results from a student finding the mean of the two means and misapplying an inequality to the scenario. This answer makes an unjustified assumption that there are more females than males.

Choice C is not the correct answer. This answer results from a student finding the mean of the two means and misapplying an inequality to the scenario. This answer makes an unjustified assumption that there are more males than females.

Question Difficulty: 
medium
Objective: 

Students must evaluate the means for two separate populations in order to determine the constraints on the mean for the combined population.