Weights of parts are normally distributed with variance 2 Measurement error is normally distributed with mean 0 and variance 0 5 2 , independent of the part weights, and adds to the part weight Upper and lower specifications are centered at 3 about the process mean (a) Without measurement error, wh...

W weights of a part and E measurement error W N w w ...

Weights of parts are normally distributed with variance 2. Measurement error is normally distributed with mean 0

Question:

Weights of parts are normally distributed with variance σ2. Measurement error is normally distributed with mean 0 and variance 0.5σ², independent of the part weights, and adds to the part weight. Upper and lower specifications are centered at 3σ about the process mean.

(a) Without measurement error, what is the probability that a part exceeds the specifications?

(b) With measurement error, what is the probability that a part is measured as being beyond specifications? Does this imply it is truly beyond specifications?

(c) What is the probability that a part is measured as being beyond specifications if the true weight of the part is 1 σ below the upper specification limit?

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