Question 1100512: . According to one of the Western Electric rules for quality control, a produced item is considered conforming if its measurement falls within three standard deviations from the target value. Suppose that the process is in control so that the expected value of each
measurement equals the target value. What percent of items will be considered conforming, if the distribution of measurements is
(a) Normal(μ, σ)?
(b) Uniform(a, b)?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Normal distribution has probability of 0.9973 between z=-3 and z=3
Uniform distribution has variance of (1/12)(b-a)^2, so sd is [sqrt(3)/6](b-a)
or sqrt(3)/6. 3 sds on either side would be sqrt(3)/2 and all would be conforming on (0, 1)
On a uniform function of (0, 10), mean would be 5 and variance 8.33 and sd 2.89. Again, 3 sd s would encompass the whole interval. 100%.
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