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.

Weight
Day Package 1 Package 2 Package 3 Package 4
Monday 23 22 23 24
Tuesday 23 21 19 21
Wednesday 20 19 20 21
Thursday 18 19 20 19
Friday 18 20 22 20

(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?

(a) These control limits are one standard error away from the centerline.
(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 based on the 1-sigma limits, although there's a significant chance with 1-sigma limits that the chart is sending a false positive out-of-control signal.