Problem

Express the confidence interval $28.2 \% \pm 5.7 \%$ in interval form.

Express the answer in decimal format (do not enter as percents).
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Final Answer: The confidence interval \(28.2 \% \pm 5.7 \%\), in interval form, is \(\boxed{[0.225, 0.339]}\).

Steps

Step 1 :The lower limit of the interval is calculated by subtracting the percentage error from the given percentage: \(28.2 \% - 5.7 \% = 22.5 \%\).

Step 2 :The upper limit of the interval is calculated by adding the percentage error to the given percentage: \(28.2 \% + 5.7 \% = 33.9 \%\).

Step 3 :To convert these percentages to decimal format, we divide by 100. So, the lower limit in decimal format is \(22.5 \% / 100 = 0.225\).

Step 4 :Similarly, the upper limit in decimal format is \(33.9 \% / 100 = 0.339\).

Step 5 :Final Answer: The confidence interval \(28.2 \% \pm 5.7 \%\), in interval form, is \(\boxed{[0.225, 0.339]}\).

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