How to minimize sum of probabilities coming from Z-score

[daviti.chuguashvili5083@e]

Assuming the variance to remain constant, state where the process
average should be located to minimise the fraction nonconforming. What would
the value of the fraction nonconforming be under these conditions? (data are normally distributed)

Variance = 77.92
Upper Limit = 20
Lower Limit = 0 [math]minize P[ (20-\bar{x})/77.92 < Z < (0-\bar{x})/77.92 ] = minimize( P[Z> (20-\bar{x})/77.92] + P[Z < (0-\bar{x})/77.92 ]) = ...???[/math]

 

[Harry_the_cat]

Is this the whole question? Is there a context or earlier parts of the question?

 

[daviti.chuguashvili5083@e]

Is this the whole question? Is there a context or earlier parts of the question?

Yes, it has but that's totally enough. I just need to solve this equation above

 

[Harry_the_cat]

It isn't enough to be able to help you. The context is very important. What does "nonconforming" refer to?