Silly String is a popular kids\" toy, but it's also an improvisational tool used by troops in Irag to detect invisible tripwires that trigger explosive devices. Silly String is extruded through the nozzle of an asrosol can. A production variable for Silly String is its spray rate, the amount of string delivered per unit of time. Suppose that the quality control manager at Just for Kicks, the manufacturer of Silly String, monitors spray rate by pulling a randem sample of 15 cans of Silly String from the production line each shift. Each can is tested in the aerosol lab to cbtain its spray rate (measured in grams per second). The sample means for 20 consecutive shifts are shown on the following graph. @ a 040 4# Center Line 0.28 [ = & Y o ucL w T = A =T 5 ona4 QO LCL 0.32 0.20 (\\:) * o 4 g 12 18 20 SAMPLE NUMBER The mean and standard deviation of the spray rate are unknown to the quality control manager. The overall sample mean is x = 0.336, and the average sample range is R = 0.126. Selected rows from the Factors for i and R Control Charts table in your text are displayed in the following table. Sample Size n d2 d3 10 3.078 0.797 15 3.472 0.756 20 3.735 0.729 25 3.931 0.708 Source: American Society for Testing and Materials, ASTM Manual on Presentation of Date and Control Chart Analysis, Philadelphia, PA, 1976. An estimate of the standard deviation o of the spray rate is Add the center line, lower control limit, and upper control limit to the chart. The quality control engineer uses the x chart to identify whether or not the production process is in a state of control. He concludes that the process is because