Once you know the lowest and highest possible percentages, how can you use the total of 2,000 customers to estimate the lowest and highest possible numbers of customers who favor the system?

Change each percentage to a decimal (for example, 67% becomes 0.67). Then multiply each decimal by 2,000 to get the corresponding number of customers.

In Desmos, type 0.67*2000 and note the output. This represents the smallest likely number of customers per week who favor the new system based on the survey.

Then type 0.77*2000 and note the output. This represents the largest likely number of customers per week who favor the new system. Use these two values as the endpoints of the interval and pick the answer choice whose range matches them.

The survey result is 72% with a margin of error of ±5 percentage points.

That means the true percentage of customers who favor the new system is likely between:

• Lower bound: $72\%-5\%=67\%$
• Upper bound: $72\%+5\%=77\%$

So the estimated proportion of all customers who favor the new system is between 67% and 77%.

The store serves about 2,000 customers per week.

To turn the percentage interval into a number-of-customers interval, multiply each end of the percentage range (in decimal form) by 2,000:

• Lower bound (as an expression): $0.67 \times 2000$
• Upper bound (as an expression): $0.77 \times 2000$

These give the approximate minimum and maximum number of customers who might favor the new system.

Now compute the bounds:

• Lower bound: $0.67 \times 2000 = 1340$
• Upper bound: $0.77 \times 2000 = 1540$

So the best interval estimate for the number of customers per week who favor the new system is 1,340 to 1,540.