SunTech Co. is developing a new window film that will prevent windows from shattering upon impact. The specifications on the film thickness are 370 ± 10 µm (micrometers). The film is made up of three layers: a dyed polyester film, metallic lining, and a scratch resistant coating. Data collected from the production of each layer component are presented in the table below. The specifications for each component are as follows (all measurements shown are in µm):
Polyester film 100 ± 5
Metallic lining 120 ± 2
Scratch-resistant coating 150 ± 3
a. Using the 50 data points provided for each component, estimate the mean, variance, and
Standard deviation for each component and also for the final assembled film thicknesses.
b. For each component calculate the estimated percentage of the relevant production output that will be outside the stipulated specification limits
c. Estimate the percentage of the assembled films that will be outside the stipulated specification limits
d. Assuming that the production distributions for each of the three components can be centered on the relevant target specifications, recommend a set of revised assembly specifications that will ensure that no more than 1% of the films will be too thick and no more than 1% of the films will be too thin.