The Confidence Interval for a Population Pencentage Is Generated from the Inequality

Multiple Choice

The confidence interval for a population pencentage is generated from the inequality $|\mathbf{p}-\hat{\mathbf{p}}|<\mathrm{E}$ , where $\mathrm{E}$ is the margin of error. Construct a $95 \%$ confidence interval for the population percentage using the given information.
-Percentage of false positives generated by a new diabetes screening test, $\hat{\mathrm{p}}=8.5 \%, \mathrm{E}=4.6 \%$

A) $3.7 \%< p<13.2 \%$
B) $4.1 \%< p<13.0 \%$
C) $4.1 \%< p<13.2 \%$
D) $3.9 \%< p<13.1 \%$