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Webster Chemical Company produces mastics and caulking for theconstruction industry. The product is blended in large mixers andthen pumped into tubes and capped. Management is concerned aboutwhether the filling process for tubes of caulking is in statisticalcontrol. The process should be centered on 8 ounces per tube.Several samples of eight tubes were? taken, each tube was? weighed,and the weights in the table below were obtained.

the ounces of caulking per tube data.

Tube number
Sample	1	2	3	4	5	6	7	8
1	7.58	8.34	8.02	7.94	8.44	7.67	7.81	8.11
2	8.33	8.17	8.08	8.51	8.41	8.28	8.09	8.16
3	7.89	7.77	7.81	8.04	8.00	7.89	7.93	8.09
4	8.24	8.18	7.83	8.03	7.90	8.16	7.97	8.07
5	7.87	8.13	7.92	7.99	7.94	7.81	8.14	7.88
6	8.13	8.14	8.11	8.13	8.14	7.99	8.13	8.14

the table of factors for calculating? three-sigma limits for thex over bar x?-chart and? R-chart.

Factors for calculating? three-sigma limits for the

x overbarx?-chart

and? R-chart.

Size of Sample? (n)	Factor for UCL and LCL for x overbarx?-chart ?(Upper A 2A2?)	Factor for LCL for? R-Chart ?(Upper D 3D3?)	Factor for UCL for? R-Chart ?(Upper D 4D4?)
2	1.880	0	3.267
3	1.023	0	2.575
4	0.729	0	2.282
5	0.577	0	2.115
6	0.483	0	2.004
7	0.419	0.076	1.924
8	0.373	0.136	1.864
9	0.337	0.184	1.816
10	0.308	0.223	1.777

a. Assume that only six samples are sufficient and develop thecontrol charts for the mean and the range.

Set up the? R-chart by specifying the center line and?three-sigma control limits below. ?(Enter your responses rounded tothree decimal? places.)

?R-chart
UCL Subscript Upper RUCLR	equals=
Upper R overbarR	equals=
LCL Subscript Upper RLCLR	equals=