a. What is the process capability index? b. Compute the process capability ratio Please show your work

Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (in.) from the last six samples are Bottle Sample 1 2 3 4 1 0.618 0.581 0.578 0.589 2 0.583 0.611 0.604 0.590 3 0.607 0.624 0.604 0.619 4 0.573 0.590 0.622 0.580 5 0.605 0.586 0.609 0.574 6 0.573 0.577 0.582 0.576 Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. Suppose that the specification for the bottle neck diameter is 0.600 +0.050 in, and the population standard deviation is 0.013 in