You have a sample percentage and a margin of error of $\pm 4$ percentage points. What are the lowest and highest percentages that could reasonably represent all voters?

Take each end of your percentage range and multiply by 62,000, the total number of registered voters. Which answer choice best matches that range?

In Desmos, type 280/500 and note the decimal result; this is the sample proportion who favor the expansion.

In a new line, type (0.56 - 0.04)*62000 (using the sample percentage minus the margin of error), and observe the output. This is the smallest reasonable number of voters who might favor the expansion.

In another line, type (0.56 + 0.04)*62000, and observe the output. This is the largest reasonable number of voters who might favor the expansion; choose the option that best matches the range between the two Desmos results.

The poll surveyed 500 voters and found that 280 favor the park expansion.

Compute the sample proportion:

• $280$ out of $500$ is

• As a percentage, $0.56 = 56\%$.

So the poll’s estimate is that about $56\%$ of registered voters favor the expansion.

The margin of error is $\pm 4$ percentage points. That means the true percentage could be as low as $56\% - 4\%$ or as high as $56\% + 4\%$.

Compute the endpoints:

• Lower end: $56\% - 4\% = 52\%$
• Upper end: $56\% + 4\% = 60\%$

So the true percentage who favor the expansion is likely between $52\%$ and $60\%$.

There are $62{,}000$ registered voters in the county.

Use the percentage range to find how many voters this represents:

So it is reasonable that the number of voters who favor the expansion is somewhere between about $32{,}240$ and $37{,}200$.

The answer choice that correctly describes this situation should:

• Give a range, not an exact number.
• Use values that are close to $32{,}240$ and $37{,}200$ (rounded to the nearest thousand).

That corresponds to "Between approximately 32,000 and 37,000 registered voters likely favor the park expansion."