Softdrink bottles are filled at a plant. The filling machine has a standard deviation of 0.05liters.
a) What target fill volume should you set to have 99% of your bottles filled to 2 liters or more?
b) The maximum capacity of the bottles is 2.2 liters. Assuming you use the target value calculated
in a) What percentage of your bottles will exceed that limit and ‘overflow’?

Question

Softdrink bottles are filled at a plant. The filling machine has a standard deviation of 0.05liters. 
a) What target fill volume should you set to have 99% of your bottles filled to 2 liters or more?  
b) The maximum capacity of the bottles is 2.2 liters. Assuming you use the target value calculated 
in a) What percentage of your bottles will exceed that limit and ‘overflow’?

kropot72 · Answer

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About 99% of the area is included within a distance of plus and minus 3 standard deviations from the mean. The target fill volume (the mean volume) should be set to
2.00 + (3 * 0.05) = ? liters
The maximum capacity of the bottles (2.20 liters) is one standard deviation above the target fill volume. The shaded area under the distribution curve is about 15.87% of the total area under the curve.