explain in detail on how to solve each problem. I need to know how to do them for my upcoming test. show your work

Scenario: The production manager at a bottle filling company is using and Average and Range Chart (with subgroups of size 4) to monitor the filling process for 12-ounce bottles (see the charts below). The filling tolerance is important because the nutrition label on the bottle is based on a fill volume of 12 ounces. The design standard for the product calls for a fill target of 12 ounces + 0.10 ounce. Xbar-R Chart for Bottle Filling Process 12 10 ua= 12.05 12.00 X=12.01 11.95 11 90 La= 8 9 10 11 12 13 14 15 Sample number ua= R=0.1267 01 0.0 La=0 9 10 11 12 13 14 15 Sample number 1 . 29 What is the Upper Control Limit for the Range Chart? Show your answer to two decimal places. UCL = Du (R ) = (2.282) (. 1267) 12.23 What is the Upper Control Limit for the Average Chart? Show your answer to two decimal places. U CL ( X ) = 12. 01 + 1, 72 95x1267 ) - m 1 1 . 92 What is the Lower Control Limit for the Average Chart? Show your answer to two decimal places. LCL -- 12. 01 - ( , 72 9) ( .126 7 ) + Trup True or False. This is a stable (in-control) process. The standard deviation for this process data is 0.05667. What is the Cpk for this process? Show your answer to two decimal places. Is the process capable