please show any work so i can understand the process thanks so much!

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 0.612 0.597 0.593 0.611 0.575 0.601 0.570 0.608 0.598 0.611 0.604 0.595 0.578 0.605 0.609 0.605 5 0.622 0.582 0.608 0.614 6 0.602 0.617 0.602 0.613 AN Click the icon to view the table of factors for calculating three-sigma limits for the X-chart and R-chart. Assume that only these six samples are sufficient, and use the data to determine control limits for an R- and an X-chart. Compute the range R and the sample mean x for each sample. (Enter your responses rounded to three decimal places.) 1 4 R Sample 1 on N 0.612 0.575 0.598 0.578 0.622 0.602 Bottle 2 3 0.597 0.593 0.601 0.570 0.611 0.604 0.605 0.609 0.582 0.608 0.617 0.602 3 4 0.611 0.608 0.595 0.605 0.614 0.019 0.038 0.016 0.031 0.603 0.589 0.602 0.599 6 0.613 Factors for calculating three-sigma limits for the x-chart and R-chart (n) Factor for LCL for R-Chart (D3) Factor for UCL for R-Chart (D4 Size of Sample Factor for UCL and LCL for X-chart (A2) 2 1.880 3 1.023 4 0.729 5 0.577 6 0.483 7 0.419 8 0.373 9 0.337 10 0.308 0 0 0 0 0 0.076 0.136 0.184 0.223 3.267 2.575 2.282 2.115 2.004 1.924 1.864 1.816 1.777