Quality System Case

You are working for the ABC Operations System as a quality manager. Your team is currently examining a new product, ABC Perfect filter, which can perfectly prevent any virus, such as COVID-19 virus, to figure out the products conformance quality. The most challenging part for the product is the filters length of a special fiber.

If the specification is such that no filter should be greater than 2.4 millimeters, assuming that the lengths of fiber are distributed normally, what fraction of the output is expected to be greater than this length? What if there is an upper and lower specification, where the upper length limit is 2.4 and the lower length limit 1.4, what fraction of the output is expected to be out of tolerance?

Quality System Sample Information Sample #2 Sample #3 Sample #4 Sample #1 1.9 1.8 2.1 2.1 2 2.2 2.4 2 1.9 2.1 2.2 2.4 1.8 2.2 2.1 1.7 2.2 1.9 2.1 2.2 1.7 1.8 2 2 2 2.1 1.8 1.6 1.9 1.6 1.7 2 1.7 1.8 1.9 2.1 1.8 1.6 1.9 2.2