Step 1: The question targets the routine vitamin K prophylaxis dose used in the delivery room for every baby.
Step 2: A baby is born with very little vitamin K. Reasons include scanty body fat where the vitamin is stored, minimal vitamin K in mother's milk, a germ-free intestine that has no bacteria to make the vitamin, an underdeveloped liver, and weak transfer across the placenta.
Step 3: Without adequate vitamin K, the liver cannot make the clotting factors that stop bleeding, putting the infant at risk of dangerous brain, gut and skin haemorrhage in the first 7 days of life.
Step 4: Standard practice is therefore to inject $1\ mg$ of vitamin K into the muscle of every newborn right after birth. Larger amounts such as 5, 10 or 15 mg are not used for this purpose.
\[\boxed{1\ mg}\]