Three-dimensional (3D) printing is a manufacturing technologythat allows the production of three-dimensionalsolid objects through a meticulous layering process performedby a 3D printer. 3D printing has rapidly become atime-saving and economical way to create a wide varietyof products such as medical implants, furniture, tools, andeven jewelry. The article Process Capability Analysis ofCost Effective Rapid Casting Solution Based on ThreeDimensional Printing (MIT Intl. J. Mech. Engr., 2012:3138) considered the production process of metal castingsby using a 3D printer. Data was collected on 16batches(each having two castings), where the outer diameter of eachcasting (in mm) was recorded. The target diameter of eachcasting was 60mm. The resulting data is given here:Batch x1 x2 1 59.664 59.675 2 59.661 59.648 3 59.679 59.652 4 59.665 59.654 5 59.667 59.678 6 59.673 59.657 7 59.676 59.661 8 59.648 59.651 9 59.681 59.67510 59.655 59.67211 59.691 59.67612 59.682 59.65113 59.651 59.68214 59.668 59.68515 59.691 59.68216 59.661 59.673Apply the supplemental rules suggested in the text to thedata. Are there any out-of-control signals?

Chapter 7: The Normal Distribution Random samples of data from a Normal Distribution whose mean µ = 64.5 and standard deviation σ = 2.5 Shortcut notation N(64.5,2.5). This distribution might represent heights of women from some population Smoothed out histograms whosearea under the curve is equal to 1 describe the overall pattern (distribution) of the population of data on that variable. Understand the 68 –95 –99.7 Rule on page247-248 of your text. Normal Distribution Curves(symmetricand bell-shaped) then according to the 68 – 95 – 99.7 rule: Approximately 68% of the data falls within one stdev of the mean. Approximately 95% of the data falls within two stdev of the mean. Approximately 99.7% of the data falls within t