For 120 consecutive days, a process engineer measured the temperature of champagne bottles as they were made ready for serving. Each day, she took a sample of 8 bottles. The average across all 960 bottles (120 days, 8 bottles per day) was 46 degrees Fahrenheit. The standard deviation across all bottles was 0.8 degrees Fahrenheit.

What would be the center line?

The center line for the temperature data of champagne bottles measured over 120 days is the mean temperature, which is 46 degrees Fahrenheit. This value is used in quality control to represent the expected value of a dataset.

Explanation:

The question at hand involves understanding statistical measures related to temperature data. Since the average temperature recorded over 120 consecutive days for 960 bottles of champagne is 46 degrees Fahrenheit, this value represents the center line, which is the mean of the dataset. It is crucial in quality control and process monitoring to use the mean temperature as the center line on a control chart, for example, because it signifies the expected value around which individual measurements are distributed.

The other detail provided in the question is the standard deviation, which is 0.8 degrees Fahrenheit. This is a measure of the dispersion of the temperatures around the mean. In process control, this would help determine control limits, but for identifying the center line, only the mean is relevant.

It is important to remember that for the given dataset of the temperature of champagne bottles, the center line would be set at the mean temperature, which is 46 degrees Fahrenheit.