Is my installation of Xcode correct? I recently downloaded an Xcode 4.4 DMG file in Apple's Developer site and then opened it and ran Xcode.  I then copied the Xcode app to my Applications folder.  By doing that way, can I assume that it's already installed?

When I type "xcode" in Spotlight, it does see the Xcode app.

Your thoughts?
It's a bit of a strange question to ask if you aren't experiencing any problems.

Yes, that's how you install Xcode when downloading from the developer centre.  However unless you need to run a beta version you're probably better off installing Xcode from the App Store, where you can benefit from update notifications and delta upgrades.