The town has 18,000 registered voters. How can you check what percentage of 18,000 each answer choice represents?

Once you know the percentage that each answer choice corresponds to, compare those percentages to your interval from the margin of error. Which one falls inside that interval?

In Desmos, type 0.58*18000 and 0.66*18000 on separate lines. These outputs give the lower and upper bounds on the number of voters consistent with the 58%–66% range.

Now type each answer choice (9540, 10800, 12600, 8460) on separate lines. Look to see which of these four numbers lies between the two bounds you found in the previous step; that is the reasonable estimate.

The poll result is 62% with a margin of error of ±4 percentage points.

So the likely range for the true percentage of voters who would vote "Yes" is:

That means the true proportion is likely between 58% and 66%.

A reasonable estimate for the number of "Yes" voters should correspond to a percentage between 58% and 66% of the 18,000 voters.

So each answer choice should be viewed as:

• (answer choice) ÷ 18,000 = fraction of voters who would vote "Yes".

We will check which choice gives a percentage between 58% and 66%.

Compute the fraction each answer choice represents of 18,000, then convert to a percent:

• A) $\frac{9{,}540}{18{,}000} = 0.53 = 53\%$
• B) $\frac{10{,}800}{18{,}000} = 0.60 = 60\%$
• C) $\frac{12{,}600}{18{,}000} = 0.70 = 70\%$
• D) $\frac{8{,}460}{18{,}000} = 0.47 = 47\%$

Now compare each of these percentages to the plausible range 58% to 66%.

From the previous step:

• 53% (choice A) is below 58%.
• 60% (choice B) is between 58% and 66%.
• 70% (choice C) is above 66%.
• 47% (choice D) is below 58%.

Only 60% lies within the 58%–66% interval. Therefore, the reasonable estimate for the number of voters who would vote "Yes" is 10,800 (choice B).