Sample ?Size, n	Mean? Factor, A2	Upper? Range, D4	Lower? Range, D3
2	1.880	3.268	0
3	1.023	2.574	0
4	0.729	2.282	0
5	0.577	2.115	0
6	0.483	2.004	0
7	0.419	1.924	0.076
8	0.373	1.864	0.136
9	0.337	1.816	0.184
10	0.308	1.777	0.223
12	0.266	1.716	0.284

Refer to Table S6.1 - Factors for Computing Control Chart Limits(3 sigma) for this problem.

?Thirty-five samples of size 7 each were taken froma? fertilizer-bag-filling machine. The results? were:Overall mean? = 60.75 ?lb.; Average range Upper R(with a bar over it) ?= 1.64 lb.

?a) For the given sample? size, the control limits for?3-sigma (x with a bar overit) chart ?are:

Upper Control Limit ?(UCL - subscript x) ?=? lb. ?(round your response to threedecimal? places).

Lower Control Limit ?(LCL - subscript x)?= ?lb. ?(round your response to threedecimal? places).

?b) Determine the upper and lower control limits ofthe? R-chart, where sigma? ?= 3.

The control limits for the? 3-sigma R-chart? are:

Upper Control Limit ?(UCL - subscript x) ?=? lb. ?(round your response to threedecimal? places).

Lower Control Limit ?(LCL - subscript x) ?=? lb. ?(round your response to threedecimal? places).