A hospital in a developing nation is forced to manually put the flu shot vaccine into syringes. The recommended dosage for the flue shot is 0.5mL. The local health authorities define all syringes that have less than 0.45 ml or more than .55 mL as defective. In a sample of 100 syringes, the hospital's 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.

a) what is the process capability index Cp of the manual filling process?

b) What percentage of the manually filled syringes will be outside the spcification limints provided by the local health authorities, i.e., P(Dosages <0.45ml) = P(Dosages>0.55ml)?

c) To what level would the hospital have to reduce the standard deviation of the operation if his goal were to obtain a process capability index of Cp = 4/3 = 1.3333 (i.e., get 63 defects per million)?