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 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.
What percentage of the manually filled syringes will be outside the specification limits provided by the local health authorities? (Please answer in decimal form.)