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Six Sigma Task I need help with

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Hello all,


I would like to get some help on a basic task regarding Six Sigma. This is a question from a University and maybe you could guide me through :) 


The production of gold bars corresponds exactly to the theoretical assumptions of 6 Sigma production. The weight of the gold bar must not be less than 500 grams. Exceptions are the extreme cases that are acceptable according to 6 σ theory.


1) How many gold bars out of one million produced are therefore lighter than 500 grams?
2) The scale on which the gold bars are weighed during production has an accuracy (corresponds to the sigma value in this task) of one per mille of the target weight. How much does a gold bar weigh on average?
3) Gold bar production currently has a 2% return on sales. By how many percent would it change if the scales were ten times more accurate and the material costs were 95% of the total costs?


Thanks and best regards


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