Oops! I spoke too soon.
What I really wanted was a surface that curved down into the "valley", so to speak, not up over the "mountain", which is what the curve that you created does.
So I went back and extracted a curve and drew a line across the widest part (it turns out that this line didn't do me any good)...step 1. I extruded a curved surface "sideways"...step 2. I then extruded a curve from the same curve, but up and down...step 3. Then I used the boolean merge command to get a surface. I deleted off all the unwanted parts...step 4. Finally, I tried to move the surface to the top of the tube to cap off the internal hole. Unforunately, the surface and the hole don't quite line up...step 5. I suspect that all this is caused by the fact that the curve is not perfectly symmetrical from side to side.

I wish there was a command that would just "stretch" a surface across the curve from side to side without having to go through all the intermediate steps.

Is it possible to do what I'm trying to do?

Frustrated,
Mark