please answer all 6 parts. please explain & number all 6 answers thank you.

West Battery Corp. has recently been receiving complaints from retailers that its 9-volt batteries are not lasting as long as other name brands. James West, head of the TQM program at West's Austin plant, believes there is no problem because his batteries have had an average life of 40 hours, about 10% longer than competitors models. To raise the lifetime above this level would require a new level of technology not available to West. Nevertheless, he is concerned enough to set up hourly assembly line checks. Previously, after ensuring that the process was running properly, West took samples of 5 9-volt batteries for 25 test to establish the standards for control chart limits. Those 25 tests are shown in the following table: Sample Data Hour Sample Taken 1 1 2 3 4 5 6 7 8 9 10 11 123 40 392288738938 34 40 45 49 26 41 34 59 3 2 46 53388228238 41 60 42 48 44 44 30 This exercise contains only parts a and b. 59 4 40 39 47 4985538828868 40 40 30 41 37 47 8888 35 29 20 26 44 65465633885883 39 32 36 38 34 33 35 37 41 37 30 31 26 52 R 8 14 X 41.4 40,0 33.8 15 41.2 40 28 14 23 36.8 47.8 34.2 Hour Sample Taken 40.6 36.0 40.8 28 41.0 27 42.4 19 41.0 29 14 HARTRS8=2323 16 17 18 19 15 47 33 42 28 21 9 -485345=2385 1 25 31 46 252845182885N 20 51 40 41 38 31 39 47 31 43 37 44 41 37 -575859839987 +38738833877 5552788858 24 39 40 39 Sample Data 43 30 46 38 40 4 48 31 48 23 49 32 30 39 48 39 5 41 40 49 46 37 41 40 30 x 40.0 43.8 38.0 36.8 41 38.8 36 42.8 42.4 38.8 39.0 38.6 38 41 40.0 53 42.8 R 16 29858 16 21 24 7 21 NDUNN 18 16 2 2 14 Sample Mean Factor, Size, n A 1.880 1.023 0.729 2345678992 10 12 0.577 0.483 0.419 0.373 0.337 0.308 0.266 Upper Range, D4 3.268 2.574 2.282 2.115 2.004 1.924 1.864 1.816 1.777 1.716 Lower Range, D3 0 0 0 0 0 0.076 0.136 0.184 0.223 0.284 a) For the given data, the For the given data, mean range = With z=3, the control limits for the mean chart are: UCL; = LCL; = = hours (round your response to three decimal places). = hours (round your response to two decimal places). hours (round your response to three decimal places). hours (round your response to three decimal places). The control limits for the range chart are: UCLR = LCLR hours (round your response to two decimal places). hours (round your response to two decimal places)