A margin of error gives a plausible range around a sample estimate for the population mean. A random sample followed by a question about all customers signals that the sample average is an estimate, not an exact value for everyone. Subtract and add the margin, then match both endpoints. A narrower range leaves out values the margin still allows.
Hints
- Hint 1
The sample mean is the average for the customers measured. The population mean is the average for all customers. Since the sample was chosen at random, which mean does its average help you estimate?
- Hint 2
The margin of error extends below and above the sample estimate. Subtract it to find the lower endpoint, then add it to find the upper endpoint. What range do you get for the mean of all customers?
Step-by-step
Build the margin-of-error interval
Step 1Connect the sample to all customers
No Desmos needed. Each endpoint takes only one subtraction or addition. The sample mean of minutes is the average for the selected customers. Because the sample was randomly chosen from café customers, it estimates the population mean, the average for all the café’s customers. It does not fix that mean exactly.
- Step 2
Find both plausible endpoints
The margin of error is how far the population mean could reasonably be from the estimate in either direction. So subtract and add the margin. Subtract from for the lower endpoint:
Add to for the upper endpoint:
- Step 3
Match the interval to the claim
The range applies to the mean for all customers, not to each customer’s wait. Starting the range at would leave out plausible means below the sample average. The mean waiting time for all café customers is best supported as between and minutes. Choice B.