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For 50 consecutive days, a process engineer has measured the weight of a component after it has been coated with special paint. Each day, she takes a sample of 10 components. The average across all 500 components is 45.343019 grams. The average range across all parts is 0.0076382 grams. When constructing an X-bar chart, what would be the centerline, and what would be the upper and lower control limits

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Answer:

UCL (X-bar) = X mean+ (A2 x R-bar)

LCL (X-bar) = X mean -(A2 x R-bar)

Center line = Mean

A2 for sample size of 10 = 0.308

X mean = 45.343019

R bar = Average of range = 0.0076382

UCL (X-bar) =45.343019+(0.308*0.0076382) = 45.3453715656 grams

LCL (X-bar) = 45.343019-(0.308*0.0076382) = 45.3406664344 grams

Center line = Mean = 45.343019

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