Comment: Officially, the police do not shoot to kill. They shoot to stop the attack. This means continuous firing until the attacker stops moving aggressively. The number of hits that will stop an attacker's aggressive movements varies with the amount of damage each hit inflicts. The amount of inflicted damage necessary to stop aggressive movements is generally massive damage to critical organs. Massive damage to critical organs increases the chances that the attacker will die.
The movie version of "bang...fall down dead" is a myth. As a poster wrote, the attacker in this story went to his uncle's apartment after suffering lethal wounds. That's more like reality.
As to immediate acting tranquilizers or some other disabling drug, where exactly would a person have to be hit for such a drug to act immediately? Under the stress of a deadly attack, would an officer be able to deliver the tranquilizing shot to just the right spot, assuming it is exposed in the first place?