Upper and lower warning limits are often established for measurements on manufac

Question

Upper and lower warning limits are often established for measurements on manufactured products. Usually if X~N(,), these are set at =(+/-)1.96 so that 5% of the product is outside the warning limits. Discuss the proportion of the product outside the warning limits if the mean of the process increases by .4 standard deviations. Upper and lower warning limits are often established for measurements on manufactured products. Usually if X~N(,), these are set at =(+/-)1.96 so that 5% of the product is outside the warning limits. Discuss the proportion of the product outside the warning limits if the mean of the process increases by .4 standard deviations.

Explanation / Answer

As we can see from the z table that at -/+ 1.96 the p value is 95% just like the same here it is given that now we want to increase the mean by 0.4 sd and so the mean becomes

lower bound =mu= -1.96+0.4 = -1.56

upper bound =mu= 1.96+0.4 = 2.36

so., by looking at the z table the area is = 0.9314826 (i.e. between z=-1.56 and +2.36) which is under the curve and so 1-0.9314826 =0.0685174 i.e. 6.85%  of the product is outside the warning limits if we increase the mean by 0.4 sd.

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