Since the featured images at Carbon adapt to the dimensions of the browser window, there is no standard size for them. You should find a balance between quality and file size, and this may vary depending on the image. For the demo we use images with dimensions of about 1200 x 800 pixels.
In any case, if you use large sized images, we recommend an image optimizer web app which is free to use and provides great results:
http://kraken.io
We just like using it ourselves, we are in no way affiliated to them, feel free to give it a try, they have a free optimizer.