It is necessary to control the percentage of solids in a product, so samples are taken randomly throughout the day and the percentage of solids is measured. Use the following 20 sets of 5 observations for this exercise:

(a) Calculate the values of

(b) Use the values of A3 and s to construct an x chart.
(c) Construct an s chart.
(d) Use the values of A2 and R to construct an x chart.
(e) Construct an R chart.
(f) Do the charts indicate that the percentage of solids in this product is in statistical control?

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Observations 69.8 71.3 65.6 66.3 70.1 68.62 2.51 5.7 71.9 69.6 71.9 71. 71.7 71.24 0.97 2.3 71.9 69.8 66.8 68.3 64.4 68.24 2.86 7.5 64.2 65.1 63.7 66.2 61.9 64.22 1.6 4.3 66.1 62.9 66.9 67.3 63.3 65.30 2.06 4.4 63.4 67.2 67.4 65.5 66.2 5.94 1.6 4.0 67.5 67.3 66.9 66.5 65.5 66.74 0.79 2.0 63.9 64.6 62.3 66.2 67.2 64.84 1.92 4.9 66.0 69.8 69.7 71.0 69.8 69.26 1.90 5.0 66.0 70.3 65.5 67.0 66.8 67.12 1.88 4.8 67.6 68.6 66.5 66.2 70.4 67.86 1.7 4.2 68.1 64.3 65.2 68.0 65.1 66.14 1.78 3.8 64.5 66.6 65.2 69.3 62.0 65.52 2.69 7.3 67.1 68.3 64.0 64.9 68.2 66.50 1.96 4.3 67.1 63.8 71.4 67.5 63.7 66.70 3.17 7.7 60.7 63.5 62.9 67.0 69.6 64.74 3.53 8.9 71.0 68.6 68 67.4 71.7 69.36 1.88 4.3 69.5 61.5 63.7 66.3 68.6 65.92 3.34 8.0 66.7 75.2 79.0 75.3 79.2 75.08 5.07 12.5 77.3 67.2 69.3 67.9 65.6 69.46 4.58 11.7 2 2 2 4 T, , and R