Question: 1. A quality analyst wants to construct a sample mean and range charts for controlling a packaging process. He knows from past experience that when
1. A quality analyst wants to construct a sample mean and range charts 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 he collected appear below in ounces.
| 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 20 ounces, the control chart is based on what value of z?
(b) With a value of z that would provide 99.73% confidence, construct an Xbar and R charts for this process. what do you conclude about the process is it in control?
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