An orchard has 1,200 apple trees. A random sample of 50 of... | SAT Inference from sample statistics and margin of error Question, Answer Explained

Question bank / Inference from sample statistics and margin of error

Math · Problem-Solving and Data AnalysisHard

An orchard has $1{,}200$ apple trees. A random sample of $50$ of the trees had a mean yield of $84$ apples per tree, with an associated margin of error of $6$ apples per tree. Which of the following is a plausible value for the total number of apples produced by all $1{,}200$ trees?

$4{,}500$

$91{,}200$

$96{,}000$

$109{,}200$

Show answer and explanation

Answer: C

Plausible values for the mean yield of all the trees are $84 \pm 6$ , or $78$ to $90$ apples per tree. Multiplying by $1{,}200$ trees, plausible totals range from $93{,}600$ to $108{,}000$ apples. Only $96{,}000$ , which is $80$ apples per tree, is in this range.

Choice D is close to the top of the range, but $\frac{109{,}200}{1{,}200} = 91$ apples per tree, which is above the greatest plausible mean of $90$ .

Why the other choices are wrong

A. This uses only the 50 sampled trees, not all 1,200 trees in the orchard.
B. 91,200 is 76 apples per tree, which is below the lowest plausible mean of 78.
D. 109,200 is 91 apples per tree, which is above the greatest plausible mean of 90.

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