A process is in control and has a normally distributed output distribution with mean of 1000 and a standard deviation of 100. The upper and lower specification limits for the process are 1060 and 940, respectively. Assuming no changes in the behavior of the process, what percentage of the
Output will be unacceptable?
A) 54.86%
B) 45.14%
C) 38.49%
D) 61.51%

Question

Quizplus · Accepted Answer

The percentage of output that is unacceptable is the area under the normal distribution curve that is outside the specification limits. This area can be calculated using the standard normal distribution (z-distribution). The z-score for the upper specification limit is (1060 - 1000) / 100 = 0.6, and the z-score for the lower specification limit is (940 - 1000) / 100 = -0.6. The area under the normal distribution curve that is outside the specification limits is the area to the left of z = -0.6 and the area to the right of z = 0.6. This area can be calculated using a standard normal distribution table or a calculator, and it is found to be 0.2743. Therefore, the percentage of output that is unacceptable is 27.43%.

A Process Is in Control and Has a Normally Distributed