Question: Statistical Quality Control (20 points)

Kitty Products caters to the growing market for cat supplies, with a full line of products, ranging from litter to toys to flea powder. One of its newer products, a tube of fluid that prevents hair balls in long-haired cats, is produced by an automated machine that is set to fill each tube with 63.5 grams of paste. To keep this filling process under control, four tubes are pulled randomly from the assembly line every four hours. After several days, the data shown in the following table resulted. Set control limits for this process and graph the sample data for both the x-chart and R-chart.

1 63.50 2.00
2 63.60 1.00
3 63.70 1.70
4 63.90 0.90
5 63.40 1.20
6 63.00 1.60
7 63.20 1.80
8 63.30 1.30
9 63.70 1.60
10 63.50 1.30
11 63.30 1.80
12 63.20 1.00
13 63.60 1.80
14 63.30 1.50
15 63.40 1.70
16 63.40 1.40
17 63.50 1.10
18 63.60 1.80
19 63.80 1.30
20 63.50 1.60
21 63.90 1.00
22 63.20 1.80
23 63.30 1.70
24 64.00 2.00
25 63.40 1.50