"However, when I got home it did not fit the back of the range or the gas outlet line coming from the wall."

Wrong size or bad fitting?

1/2 inch is pretty small for gas.

First, you'll want the bigger hose for that range. Figure out the max btu - it probably says on the back of the range - or just add together all the burners and the oven. You'll probably need a 5/8 hose and not too long of one - 3 or 4 feet at most.

Buy something like this (menards link) and it comes with two different sizes of connector. There's a chart on the back to show you how many BTUs you should try to feed with each length and diameter of hose.

Use the fittings you have to figure out the size you need before you return them. There's probably only two sizes. If your fittings are too small, you need the 3/4" ones.

At our local hardware store you have to work down to what you need:
First, pick the diameter hose (you want the thickest one)
Second, pick the length (you want the shortest you can reasonably install)
Third, pick the connectors (at Menards they just put both size connectors in the bag)

Make sure you're attaching to the right spot on the range. Mine has a cap to access the regulator that has threads that look like you could use them. Then on the bottom is the "real" spot for gas hookup.

You have to screw in the adapter piece, with threads on one side and a taper on the other. Use the sealant paste for the threads. Then you attach the hose to the taper - no paste here. Same on both ends of the hose unless the adapter piece from the last range got left on the pipe stub.

so it goes:
floor/wall -> pipe -> valve -> taper adapter -> hose -> taper adapter -> range.

It might just be a simple matter of confusing outer diameter with inner diameter.

I have a Culinarian on order and just finished my gas line installation. Capital only requires a 1/2" gas connection from the wall. I did run 3/4" in the wall and came out with a reducing elbow but the spec is only 1/2" for the supply out of the wall. The flex tube spec is 5/8" per Capital's requirements. The back of the range should be 1/2" but I haven't taken delivery yet. If you go to the orange box, they have kits that have 5/8" tube in 3,4 and 5' lengths with the adapter fittings for the 1/2"NPT. If you go to the orange box during the day you should be able to find someone that can help you get the correct kit if you can't find it. I have found that the night crew is usually not what I would consider the A team.

I am sure by now you have your range hooked up but the exact part number that will work is Brasscraft CSSC45E-48 P. They have it at the orange box. The picture online in not correct. It comes with a 1/2" FIP fitting that will attach directly to the Culinarian and a 1/2" MIP fitting that will screw directly into your gas valve at the wall(assuming the gas valve is female). I assumed this was for a 36" Culinarian. I'm not sure if the larger size Culinarians also have a 1/2" connection on the back. Probably late with the info but maybe it will help someone else.