Modded SAT Question Bank
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Test
Math
Domain
Problem-Solving and Data Analysis
Skill
Inference from sample statistics and margin of error
Difficulty
Easy
ID: f4b3672a
Modded SAT Question Bank by Abdullah Mallik

A certain forest is 253 acres. To estimate the number of trees in the forest, a ranger randomly selects 5 different 1-acre parcels in the forest and determines the number of trees in each parcel. The numbers of trees in the sample acres are 51, 59, 45, 52, and 73. Based on the mean of the sample, which of the following ranges contains the best estimate for the number of trees in the entire forest?

  1. 11,000 to 12,000

  2. 12,500 to 13,500

  3. 13,500 to 14,500

  4. 18,000 to 19,000


Tip: Press CTRL/Command to toggle answer
Correct Answer: C
Rationale

Choice C is correct. The mean of the 5 samples is the fraction with numerator, 51 plus 59 plus 45 plus 52 plus 73, and denominator 5, equals 56 trees per acre. The best estimate for the total number of trees in the forest is the product of the mean number of trees per acre in the sample and the total number of acres in the forest. This is (56)(253) = 14,168, which is between 13,500 and 14,500.

Choice A is incorrect and may result from multiplying the minimum number of trees per acre in the sample, 45, by the number of acres, 253. Choice B is incorrect and may result from multiplying the median number of trees per acre in the sample, 52, by the number of acres, 253. Choice D is incorrect and may result from multiplying the maximum number of trees per acre in the sample, 73, by the number of acres, 253.

 

Question Difficulty: Easy
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