Motorola used the normal distribution to determine theprobability of defects and the number of defects expected in aproduction process. Assume a production process produces items witha mean weight of 10 ounces.
(a)
The process standard deviation is 0.21, and the process controlis set at plus or minus one standard deviation. Units with weightsless than 9.79 or greater than 10.21 ounces will be classified asdefects. (Round your answer to the nearest integer.)
Calculate the probability of a defect. (Round your answer tofour decimal places.)
Calculate the expected number of defects for a 1,000-unitproduction run. (Round your answer to the nearest integer.)
defects
(b)
Through process design improvements, the process standarddeviation can be reduced to 0.07. Assume the process controlremains the same, with weights less than 9.79 or greater than 10.21ounces being classified as defects.
Calculate the probability of a defect. (Round your answer tofour decimal places.)
Calculate the expected number of defects for a 1,000-unitproduction run. (Round your answer to the nearest integer.)
defects
(c)
What is the advantage of reducing process variation, therebycausing process control limits to be at a greater number ofstandard deviations from the mean?
Reducing the process standard deviation causes no change in thenumber of defects.Reducing the process standard deviation causes asubstantial increase in the number ofdefects.     Reducing the process standarddeviation causes a substantial reduction in the number ofdefects.
