In my study, I found that people are influenced by detective novels and generally think it takes around 365 pages to solve a murder.
Actually, I can only give you examples of crimes. Take the case of an individual who is harassed at work for a long time, gets mad and suddenly kills someone. Another example might be a mother who kills her child who is very sick, or young people who point their weapons at one another and fire them in plain sight.
For the first type of crime, to some extent, deterrence isn't really an issue, because they are crimes committed on impulse. As for other crimes, crimes committed by organized crime, their rate of solution is generally quite low. When you hire a hitman to knock someone off... Take the Auger case; the guy who tried to kill that reporter was never found.