2 oz and standard deviation 01 oz the average net

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Unformatted text preview: X is calibrated in such a way that fill weights of containers are approximately normally distributed with mean 8.2 oz and standard deviation 0.1 oz. The average net weight of a container is advertised as 8.2 oz. A quality control standard is proposed which would specify that weights of containers must lie between 8 and 8.3 oz (it is too expensive to overfill by more than .1 oz and there might be trouble with consumer advocates if a container is under-filled by more than .2 oz). a. If the proposal were adopted, what proportion of containers would lie outside specifications? SOLUTION: P(X > 8.3, or X < 8) = 1 − P(8 < X < 8.3) = 1 − P( 8−.8.2 ≤ Z ≤ 8.30−18.2 ) 01 . = 1 − [P(Z ≤ 1) − P(Z ≤ −2)] = 1 − (0.8413 − 0.0228) = 1 − 0.8115 = 0.1885. It has been decided that the quality control standard will be adopted and that at least 86.5% of containers must meet specifications, and there are two methods of achieving this: the first is to leave the uncertainty of the filling apparatus unchanged, but to change the calibration of the apparatus to give a new mean fill weight (and to advertise this new weight as the average net weight). The second is to improve the precision of the ap...
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