a) For the given data, the x double overbarx =_____ hours(round your response to three decimal places).

For the given data, the mean range=_____ (round youre response to three decimal places).

With z=3, the control limits for the mean chartare:

UCL Subscript x overbarUCLx=_____ hours (round your response to three decimal places).

LCL Subscript x overbarLCLx= _____ hours (round your response to three decimal places).

The control limits for the range chart are:

UCL Subscript Upper RUCLR=_____hours (round your response to two decimal places).

LCL Subscript Upper RLCLR=____ hours (round your response to two decimal places).

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 45 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 1 4 5 R 1 2 4 5 44 48 40 2 24 Sample Data Hour Sample Taken 2 3 x 1 46 45 45 45 45.0 2 40 42 55 41 31 41.8 3 46 40 38 40 41 41.0 4 49 51 47 45 47 47.8 5 43 3272324344.4 6 53 58 31 48 62 50.4 7 31 29 43 44 50 39.4 8 47 81 49 39 34 48.0 8 39 47 42 42 40 42.0 10 64 39 45 42 37 45.4 11 53 48 58 40 32 45.8 12 51 43 42 38 56 47.0 13 34 64 53 39 39 45.8 This exercise contains only parts a and b. a) For the given data, the x = hours (round your response to three decimal places). Hour Sample Taken 14 15 16 17 18 19 20 21 22 23 24 25 55 49 44 45 45 44.2 48.8 43.2 42.6 47.6 47.0 6 40 31 21 27 8 27 24 18 30 3 34 48 37 43 37 48 36 43 50 48 45 45 47 54 53 36 57 45 38 35 60 45 53 47 54 44 47 42 49 35 42 44 45 44 47 45 52 28 55 51 42 35 53 45 44 47 47 R 20 19 29 20 23 11 19 19 15 4 3 12 45 34 41 43 45 57 42.8 43.8 44.0 43.8 45.2 48.2 Definition Sample Size, n 2 3 4 5 6 7 8 9 10 12 Mean Factor, A2 1.880 1.023 0.729 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