Answer:
70.94 mm is the upper control level with a 99.7% level of confidence.
Step-by-step explanation:
We are given the following data:
69, 72, 71, 70, 68
Population mean = 70 mm
Population standard deviation = 1.25 mm
We have to find the upper control level with a 99.7% level of confidence.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{350}{5} = 70[/tex]
99.7% Confidence interval:
[tex]\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.003} = \pm 2.98[/tex]
[tex]70 \pm 2.98(\frac{1.25}{\sqrt{16}} ) = 70 \pm 0.93125 = (69.06875,70.93125) \approx (69.07,70.94)[/tex]
Thus, 70.94 mm is the upper control level with a 99.7% level of confidence.
