The upper 2-sigma control limit for the sample mean chart is 24.6 ounces.
How to solve
1. Calculate the mean and standard deviation for each day:
Day Mean Standard Deviation
Monday 23.0 0.707107
Tuesday 21.0 1.414214
Wednesday 20.0 0.707107
Thursday 19.0 0.707107
Friday 20.0 1.414214
2. Calculate the overall mean (x):
x = (23.0 + 21.0 + 20.0 + 19.0 + 20.0) / 5 = 20.6
3. Calculate the upper 2-sigma control limit (UCL):
UCL = x + 2 * σ = 20.6 + 2 * 2 = 24.6
Therefore, the upper 2-sigma control limit for the sample mean chart is 24.6 ounces. This limit allows for natural variations in the packaging process while identifying significant deviations that might indicate a problem.
The Complete Question
A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that the process standard deviation is 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
Calculate upper 2-sigma x-bar chart control limit that allow for natural variations