Question

a bottled water plant uses a production process designed to fill bottles with 20 ounces of water. the population of filling volumes is normally distributed with a standard deviation of 1.3 ounces. periodically, process engineers take 20-bottle samples and compute the sample mean. what are the upper and lower control limits? suppose the last five sample means were 19.4 20.2 20.5 20.7 21.1 ounces. is the process under control?

Answer 1

The upper control limit is 20.57 ounces and the lower control limit is 19.43 ounces. The process is considered to be under control.

Step-by-step explanation:

The upper and lower control limits can be calculated using the formula:

Upper Control Limit = Sample Mean + (3 * Sample Standard Deviation)

Lower Control Limit = Sample Mean - (3 * Sample Standard Deviation)

Using the given sample means of 19.4, 20.2, 20.5, 20.7, and 21.1 ounces, we can calculate the sample standard deviation to be approximately 0.57 ounces. Plugging in the values, the upper control limit is 20.57 ounces and the lower control limit is 19.43 ounces.

Based on these control limits, we can see that all of the sample means fall within the control limits. Therefore, the process is considered to be under control as there are no points outside of the control limits.