An automatic filling machine is used to fill 1-liter bottles of
cola. The machine’s output is approximately normal with a mean of
0.99 liter and a standard deviation of 0.04 liter. Output is
monitored using means of samples of 26 observations. Use
Table-A.
a.Determine upper and lower control limits that
will include roughly 97 percent of the sample means when the
process is in control. (Do not round intermediate
calculations. Round z value to 2 decimal places. Round your answers
to 4 decimal places.)
Upper control limits: | liter |
Lower control limits: | liter |
b.Given these sample means: 1.005, 1.001, .998, 1.002,
.995, and .999, is the process in control?
Yes
No
Given values:
Mean (X-double bar) = 0.99 liter
Standard deviation (SD) = 0.04 liter
Sample size (n) = 26 observations
For 97% confidence interval, Z = 2.17
Solution:
(a) Upper and Lower control limits are calculated as,
Upper control limit = X-double bar + [Z x SD/SQRT(n)]
Lower control limit = X-double bar - [Z x SD/SQRT(n)]
Upper control limit = 0.99 + [2.17 x 0.04/SQRT(26)]
Upper control limit = 1.0070 liter
Lower control limit = 0.99 - [2.17 x 0.04/SQRT(26)]
Lower control limit = 0.9730 liter
(b) Yes, the process is in control as all the given sample means lie between the calculated values of Upper control limit and Lower control limit.
An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is...
An automatic filling machine is used to fill 1-liter bottles of cola. The machine's output is approximately normal with a mean of O.99 liter and a standard deviation of 0.04 liter. Output is monitored using means of samples of 26 observations. Use Table-A a.Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control. (Do not round intermediate calculations. Round z value to 2 decimal places. Round your answers...
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