Final answer:
The student's question involves using variable measures like the filling volume of 12-oz soda bottles and applies quality control charts (№-bar and R-bar) to monitor and manage the production process.
Step-by-step explanation:
The student's question relates to the monitoring of a production process using quality control charts. The process being measured is the filling of 12-oz bottles with soda, which is a variable measure since it refers to quantities like volume that are measurable and can vary continuously. The historical distribution of the process output, in this case, would typically be assumed to follow a normal distribution, as it's a common assumption for processes like bottle filling controlled by many random variables.
To monitor the quality of the filling line, two common types of control charts are used, the №-bar chart and the R-bar chart. The №-bar chart is used to monitor the process mean, and the R-bar chart is used to monitor the variability of the process. Together, these charts help ensure that the bottle filling process remains consistent and within specified limits.