Final answer:
The population for the administrator's question is all the students in the large middle school where vending machines are being installed. The aim is to determine the type of vending machines that would be most popular among these students.
Step-by-step explanation:
The population for the administrator's question refers to the entire group about whom she wants to gain information. In this case, since the administrator is installing vending machines in a large middle school, the population would be all the students in that school.
The type of vending machines that would be most popular among these students is the main concern, so understanding their preferences would involve possibly using a sample of that population to gather data that can be generalized back to the entire group.
Considering the administrator's purpose, it would be beneficial to use a type of sampling method such as simple random sampling, stratified sampling, or systematic sampling to ensure a representative sample of students is included in the survey to determine popular vending machine choices. Factors such as age, grade, and preferences could be considered when deciding on the sampling technique to use.