Once you have the lower and upper percentage bounds, convert those percentages into decimals and multiply by the total of 15,000 households to get a range of household counts.

After you find the lower and upper estimates for the number of households, look for the answer choice whose range matches your calculated numbers.

In Desmos, type (0.63 - 0.06) * 15000 and note the value shown; this is the lower estimate for the number of households that recycle weekly.

Type (0.63 + 0.06) * 15000 and note this value; then look for the answer choice whose interval uses the lower and upper values you just found.

The researchers found that 63% of the sampled households recycle at least once a week, with a margin of error of ±6 percentage points at the 95% confidence level.

This means the true proportion of all Greenville households that recycle is estimated to lie between:

• Lower bound: $63\% - 6\% = 57\%$
• Upper bound: $63\% + 6\% = 69\%$

Convert the percentage bounds to decimal proportions:

• $57\% = 0.57$
• $69\% = 0.69$

These represent the fraction of all 15,000 households that are expected to recycle at least once a week. So the estimated number of such households is between $0.57$ of 15,000 and $0.69$ of 15,000.

Now multiply each bound by 15,000:

• Lower bound:

• Upper bound:

So the estimated number of households that recycle at least once a week is between 8,550 and 10,350, which matches choice B.