# How to minimize sum of probabilities coming from Z-score

#### underwood

##### New Member
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

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

#### katxt

##### Active Member
First check the relationship between variance and standard deviation.