Story 1: One of my kids called 911 about 2 years ago. Either the 5yo or the 3yo (then), but both denied it. I only found out when the 911 dispatcher called back asking whether there were an emergency (No.), but insisted that since the call was placed that an officer would have to come by, so we (the two kids and I) went out in the front lawn to pull weeds and wait. I greeted the officer when he arrived and explained what must have happened. He reassured the kids that they were not in trouble, and if they have an emergency to please call 911.
Response time was probably <10 minutes. Police station is 1 mile away or so.
Story 2: Middle of summer, middle of night (1am?), cornfield, deer, slam, TREES! (whew!) mailbox, ditch. Where's the deer? Dang! Can't find it. Run home (~1/2 mile, college student, very good shape, 3 min. max). Need a gun. 30-06. Sister pulls in, "quick drive me down the road." Find the deer, dead? don't know. BLAM! Wow, that was loud. Drive back home (1/2 mile). Call Sheriff, crash/deer/gun, OK, I'll go meet the Deputy right now.
By the time I got back (1/2 mile) 4-5 neighbors from 100yards away or more were already there, along with the Sheriff's Deputy (!). Heard gunshot, called sheriff. There hadn't even been enough time for the dispatcher to get ahold of the Deputy to tell him what I told her.
Repsonse time <3 min.