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The problem asks you to express the confidence interval \( (261.4, 517.2) \) in the form of \( \bar{x} \pm ME \), where \( \bar{x} \) is the sample mean and \( ME \) is the margin of error.

Here's how to solve it:

1. The confidence interval \( (261.4, 517.2) \) means that the lower limit is 261.4 and the upper limit is 517.2.
2. To find \( \bar{x} \), take the average of the two limits:
   \[
   \bar{x} = \frac{261.4 + 517.2}{2} = \frac{778.6}{2} = 389.3
   \]
3. The margin of error \( ME \) is the distance from the sample mean \( \bar{x} \) to either limit. We can calculate it as:
   \[
   ME = 517.2 - 389.3 = 127.9
   \]

Thus, the confidence interval in the form \( \bar{x} \pm ME \) is:
\[
\bar{x} \pm ME = 389.3 \pm 127.9
\]

Would you like further details on this process?

Here are 5 related questions to explore further:
1. How do you calculate confidence intervals for a population mean?
2. What factors affect the margin of error in a confidence interval?
3. Can a confidence interval be asymmetric?
4. How is the sample size related to the width of a confidence interval?
5. How do you interpret the confidence level (e.g., 95%) in a confidence interval?

**Tip:** The larger your sample size, the smaller the margin of error will generally be, leading to a narrower confidence interval.

Express the confidence interval (261.4, 517.2) in the form of x̄ ± ME.

Learn how to express the confidence interval (261.4, 517.2) in the form of x̄ ± ME. This problem involves calculating the sample mean and margin of error, suitable for students in Grades 11-12 or college-level statistics.

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