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I am working on modelling a process that follows a normal distribution with the following specifications

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If the processes output (parts) is too short (< 17.55) or too long (> 18.44) then that part becomes useless and is scraped. I can tweak the mean parameter.

This is my question:

  1. What might be different ways I can find the optimum mean parameter such that given interval maximizes the proportion of parts satisfying the above condition
  2. Could there be a closed-form solution to this problem?

Thanks.

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