A margin of error gives a range around a sample mean; the upper endpoint is the mean plus the margin. To find a total based on that endpoint, multiply the monthly mean by the number of apartments in the entire city, using Desmos for the arithmetic. The sample size tells you how many apartments were surveyed, not how many are in the city.
Hints
- Hint 1
The margin of error is the distance from the sample mean to either endpoint of the interval. To reach the upper endpoint, do you add or subtract the given dollar amount?
- Hint 2
A mean is a total divided by a count. Reverse that relationship to find total rent, and use all apartments in the city, not just the apartments in the survey.
Step-by-step
Use the upper-end mean to find the total
Step 1Find the upper-end monthly mean
The margin of error is the distance from the sample mean of $1,120 to either end of the interval. For the upper endpoint, add $60. Type in Desmos; it displays . So the mean monthly rent to use is $1,180.
- Step 2
Turn the mean into a citywide total
A mean is a total divided by a count, so total rent = mean rent times apartment count. Use the 18,500 apartments in the city, not the sample of apartments:
- Step 3
Calculate the monthly total
Type beneath your first Desmos line. It displays , so the city's apartments would collect $21,830,000 in one month if the mean rent were at the upper endpoint. Choice C.