Question

a study was commissioned to find the mean weight of the residents in a certain town. the study found the mean weight to be 191 pounds with a margin of error of 8 pounds. which of the following is a reasonable value for the true mean weight of the residents of the town? answer 181.6 198.3 200.7 182.3

Explanation:

Step1: Recall margin - of - error concept

The true mean lies within the interval of the sample mean $\pm$ margin of error.

Step2: Calculate the lower and upper bounds

The lower bound is $191 - 8=183$ pounds and the upper bound is $191 + 8 = 199$ pounds.

Step3: Check the options

We check which option lies within the interval $[183,199]$.

• Option 181.6 is less than 183, so it is not valid.
• Option 198.3 lies within the interval $[183,199]$.
• Option 200.7 is greater than 199, so it is not valid.
• Option 182.3 is less than 183, so it is not valid.

Answer:

198.3