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Catracho Catracho
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5 years ago
A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows
from past experience that when the process is operating as intended, packaging weight is normally
distributed with a mean of twenty ounces, and a process standard deviation of two ounces. Each day
last week, he randomly selected four packages and weighed each. The data from that activity appear
below.
  see the document I uploaded
(a)
If he sets an upper control limit of 21 and a lower control limit of 19 around the target value of
twenty ounces, the control chart is based on what value of
z
?
(b)
With the UCL and LCL of part a, what do you conclude about this process–is it in control?
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Educator
5 years ago
(a)   These control limits are one standard error away from the centerline, and thus include 68.268 percent of the area under the normal distribution. There is therefore a 31.732 percent chance that, when the process is operating in control, a sample will indicate otherwise.

(b)   The mean of sample 1 lies outside the control limits. All other points are on or within the limits. The process is not in control.
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