To express the confidence interval (284.5, 497.3) in the form of \( \bar{x} \pm ME \), we need to determine the sample mean \( \bar{x} \) and the margin of error \( ME \).
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Find the sample mean \( \bar{x} \): \[ \bar{x} = \frac{\text{Lower limit} + \text{Upper limit}}{2} = \frac{284.5 + 497.3}{2} = \frac{781.8}{2} = 390.9 \]
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Find the margin of error \( ME \): \[ ME = \frac{\text{Upper limit} - \text{Lower limit}}{2} = \frac{497.3 - 284.5}{2} = \frac{212.8}{2} = 106.4 \]
Now, we can express the confidence interval as: \[ \bar{x} \pm ME = 390.9 \pm 106.4 \]
Thus, the final expression is: \[ 390.9 \pm 106.4 \]