There is no relation between the M1icon Carbine serial number and that of the M1 Rifle. In order to know which sight, we would have to see some pretty good pictures to tell if it underwent a government rebuild, which it most likely did. In this case it would have the adjustable sight and a bayonet lug extension on the barrel band. I don't have the date information, but all carbines were made during WWII. Most all of them were revised/upgraded over the years after the war, and they were in service for many years. Here is a link to a typical Type III sight that would have been installed on rebuilds as well as some later originals.
http://cgi.ebay.com/M1-Carbine-rear-...item19c78bf249