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A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be 151 pounds with a margin of error of 5 pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town?
156.9
147.7
155.2
147.5

A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be $151$ pounds with a margin of error of $5$ pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town? $\newline$ $156$ . $9$ $\newline$ $147$ . $7$ $\newline$ $155$ . $2$ $\newline$ $147$ . $5$

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Interpret measures of center and variability

Full solution

Q. A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be

151

pounds with a margin of error of

5

pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town?

\newline

156

.

9

\newline

147

.

7

\newline

155

.

2

\newline

147

.

5

Understand Margin of Error: Understand the concept of margin of error. The margin of error gives us a range in which the true mean is likely to fall. The given margin of error is $5$ pounds, which means the true mean weight is likely to be within $5$ pounds above or below the reported mean of $151$ pounds.
Calculate Range of Values: Calculate the range of reasonable values for the true mean weight. $\newline$ The lower bound of the range is $151 - 5 = 146$ pounds. $\newline$ The upper bound of the range is $151 + 5 = 156$ pounds.
Determine Values in Range: Determine which values fall outside the calculated range. $\newline$ We compare each given value to the range of $146$ to $156$ pounds. $\newline$ - $156.9$ is greater than $156$ , so it is not reasonable. $\newline$ - $147.7$ is within the range, so it is reasonable. $\newline$ - $155.2$ is within the range, so it is reasonable. $\newline$ - $147.5$ is within the range, so it is reasonable.
Identify Unreasonable Value: Identify the value that is not a reasonable estimate for the true mean weight. $\newline$ The value $156.9$ pounds does not fall within the range of $146$ to $156$ pounds, so it is not a reasonable estimate for the true mean weight of the residents of the town.

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