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).
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Calculate the midpoint \( \bar{x} \): \[ \bar{x} = \frac{368.8 + 678.8}{2} = \frac{1047.6}{2} = 523.8 \]
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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:
\[ 523.8 \pm 155 \]
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