Question 14·Medium·Inference from Sample Statistics and Margin of Error

The $58\%$ describes the sample of $600$ voters, so it estimates the percentage among all registered voters rather than fixing it exactly. The $4$-point margin of error lets that citywide percentage be $4$ percentage points below or above $58\%$. Subtract and add the margin:

So the plausible citywide percentage runs from $54\%$ to $62\%$. Don't take $4\%$ of $58\%$; the margin is added and subtracted as percentage points.

The question asks about the $12{,}000$ registered voters, not just the $600$ surveyed. Type $54\%\operatorname{of}12000$ and $62\%\operatorname{of}12000$ on separate lines in Desmos. It prints $6{,}480$ and $7{,}440$, so the plausible citywide count runs from $6{,}480$ to $7{,}440$.

Compare the choices with the plausible count interval from $6{,}480$ to $7{,}440$. Only $6{,}900$ falls inside it, so $6{,}900$ is a plausible number of registered voters planning to vote for the candidate. Apply the margin to the percent first, then apply that range to the whole population. Choice B.