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A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was 533 with a margin of error of 27 . Which of the following is a reasonable value for the true mean SAT score of graduating high school seniors?
565.7
516
493.9
564.6

A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was $533$ with a margin of error of $27$ . Which of the following is a reasonable value for the true mean SAT score of graduating high school seniors? $\newline$ $565$ . $7$ $\newline$ $516$ $\newline$ $493$ . $9$ $\newline$ $564$ . $6$

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Scale drawings: word problems

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Q. A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was

533

with a margin of error of

27

. Which of the following is a reasonable value for the true mean SAT score of graduating high school seniors?

\newline

565

.

7

\newline

516

\newline

493

.

9

\newline

564

.

6

Understand Margin of Error: Understand the concept of margin of error. The margin of error in a statistical study is the range within which we can expect the true mean to lie with a certain level of confidence. In this case, the margin of error is $27$ points.
Calculate Lower Bound: Calculate the lower bound of the mean SAT score. Subtract the margin of error from the given mean to find the lowest possible value of the true mean. Lower bound = Mean SAT score - Margin of error = $533 - 27 = 506$
Calculate Upper Bound: Calculate the upper bound of the mean SAT score. Add the margin of error to the given mean to find the highest possible value of the true mean. Upper bound = Mean SAT score + Margin of error = $533 + 27 = 560$
Determine Valid Values: Determine which of the given values fall within the calculated range. $\newline$ We have established that the true mean SAT score should be between $506$ and $560$ . Now we need to check which of the given values fall within this range. $\newline$ - $565.7$ is greater than $560$ , so it is not a reasonable value. $\newline$ - $516$ is between $506$ and $560$ , so it is a reasonable value. $\newline$ - $493.9$ is less than $506$ , so it is not a reasonable value. $\newline$ - $564.6$ is greater than $560$ , so it is not a reasonable value.

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