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There may be a typical distinctive range but it isn't a range unique to firearms. There's also real world variables at play here such as gunshots outdoors vs indoors that'd force them to broaden that range leading to more false positives.
Take an o-scope and a digital microphone setup, fire a gun, and i promise you you'll not see the same reading with anything else, But, if you're tied to an argument go ahead and do it with someone else.
Way too many variables. Are you shooting 9mm, 45, .338 Lapua, .22lr? Are you shooting from a 9 in barrel, a 16 in, a three inch? Are you using a muffler? What brand and type? What is your range to the gun shot? Is the bullet supersonic or subsonic? Does the roofers hammer make a sound that falls inside the wide range of noises? There is no way to make an accurate profile for gun shot noise.
Well when I ran destructive test we used an assortment of guns. I suppose to collect this data you would do the same thing and use the average sample across the timeline for your programs baseline. Just a guess.