Question

Express the confidence interval 368.8 < mu < 678.8 in the form of bar(x) pm ME

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Answer 1

To express the confidence interval \( 368.8 < \mu < 678.8 \) in the form of \( \bar{x} \pm ME \), we need to calculate the midpoint (the point estimate \( \bar{x} \)) and the margin of error (ME).

1. **Calculate the midpoint** \( \bar{x} \):
\[
\bar{x} = \frac{368.8 + 678.8}{2} = \frac{1047.6}{2} = 523.8
\]

2. **Calculate the margin of error** \( ME \):
\[
ME = \bar{x} - 368.8 = 523.8 - 368.8 = 155
\]
or
\[
ME = 678.8 - \bar{x} = 678.8 - 523.8 = 155
\]

Combining these results, we express the confidence interval as:

\[
\bar{x} \pm ME
\]

Thus, we write:

\[
523.8 \pm 155
\]

So, the final expression is:

\[
523.8 \pm 155
\]