A beverage company would like to use a mean chart to monitor how much liq- uid beverage it puts into each 500-ml bottle. They know from past experience that whenever this process is under control, bottle weight is normally distributed with a mean of 500 ml and a standard deviation of 2 ml. The company plans to measure samples of 25 bottles from the production line every hour, and record the mean weight of liquid beverage in the bottles.

a. If the company uses z = 3.0 as its standard for establishing the mean chart, where will the upper and lower control limits be on that chart?

b. For legal reasons, the company cannot tolerate more than 501 or less than 499 ml in each bottle. What is the process capability index value for this bottling pro- cess? What does it indicate about the process?