A hospital in a developing nation is forced to manually put the flu shot vaccine into syringes. The recommended dosage for the flu shot is 0.5mL. The local health authorities define all syringes that have less than 0.45ml or more than 0.55mL as defective.

In a sample of 100 syringes, the hospitals quality control officer finds the average dosage to be 0.5mL. The standard deviation of the dosage is 0.02 mL and the distribution of the dosages resembles a normal distribution reasonably closely.

To what level would the hospital have to reduce the standard deviation of the operation if his goal were to obtain a capability score of Cp=4/3 (i.e., get 63 defects per million)?