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

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

Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvelis Lifelong Lawn Ltd. The results were: Overall mean = 54.75 lb.; Average range R = 1.78 lb.

a) For the given sample size, the control limits for 3-sigma x chart are:

Upper Control Limit (UCLx) = ?? lb. (round your response to three decimal places).

Lower Control Limit (LCLx) = ?? lb. (round your response to three decimal places).

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

Upper Control Limit (UCLR) = ?? lb. (round your response to three decimal places).

Lower Control Limit (LCLR) = ?? lb. (round your response to three decimal places).