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 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) = 55.496 lb. (round your response to three decimal places).

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

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

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).

Sample Size, n 2 3 4 5 6 7 8 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 9 10 12