Solution from part a one sees that for 82 the auc of

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Unformatted text preview: paratus so as to reduce the uncertainty while leaving the mean fill weight (and the advertised average net weight) unchanged. b. If the first method is adopted, find an acceptable mean fill weight. SOLUTION: From part a., one sees that for µ = 8.2, the AUC of the specification interval is less that what will be asked for (0.865). First, one realizes that there could be multiple possible options for µ. Since one of them will fulfill the requirement, we ask which value of µ will maximize the AUC for the specification interval ([8,8.3]). The obvious choice based on the geometric characteristic of normal curve will be the one that is symmetric about µ. So, if µ = 8.15, the specification interval will be symmetric about the mean, yielding the max of AUC. . P(8 < X < 8.3) = P( 8−8115 ≤ Z ≤ 8.3−8.15 ) 0. 0 .1 = P(Z ≤ 1.5) − P(Z ≤ −1.5) = 2P(Z ≤ 1.5) − 1 = 2(0.9332) − 1 = 0.8664 > 0.865. Actually ∀µ ∈ [8.142, 8.158], AUC([8, 8.3]) > 0.865. c. If the second method is adopted, find an acceptable standard deviation of fill weights. SOLUTION: To increase the AUC of specification interval ([8,8.3]) without shifting the curve, one can dec...
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