A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be $163$ pounds with a margin of error of $5$ pounds. Which of the following is a reasonable value for the true mean weight of the residents of the town? $\newline$ $156$ $\newline$ $169$ . $9$ $\newline$ $169$ . $3$ $\newline$ $159$ . $5$

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

163

pounds with a margin of error of

5

pounds. Which of the following is a reasonable value for the true mean weight of the residents of the town?

\newline

156

\newline

169

9

\newline

169

3

\newline

159

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 study found the mean weight to be $163$ pounds with a margin of error of $5$ pounds. This means the true mean weight could be as low as $163 - 5$ pounds or as high as $163 + 5$ pounds.
Calculate lower limit: Calculate the lower limit of the true mean weight. $\newline$ Lower limit = Mean weight - Margin of error $\newline$ Lower limit = $163 - 5$ $\newline$ Lower limit = $158$ pounds
Calculate upper limit: Calculate the upper limit of the true mean weight. $\newline$ Upper limit = Mean weight + Margin of error $\newline$ Upper limit = $163 + 5$ $\newline$ Upper limit = $168$ pounds
Determine values in range: Determine which of the given values fall within the calculated range. $\newline$ The range of the true mean weight is from $158$ to $168$ pounds. Now we need to check which of the given values fall within this range: $\newline$ - $156$ is below the lower limit. $\newline$ - $169.9$ is above the upper limit. $\newline$ - $169.3$ is above the upper limit. $\newline$ - $159.5$ is within the range.
Select reasonable value: Select the reasonable value for the true mean weight. $\newline$ Since $159.5$ is the only value that falls within the range of $158$ to $168$ pounds, it is the reasonable value for the true mean weight of the residents of the town.