Half the total should be 4". It doesn't matter that it's not 4" on the part that is sewn down, but it sounds like yours is ¼" too narrow. For that reason, I'd start over. Your sleeve is not yet sewn on, is that correct?
Also, I always start with a 9" strip, not 8½", because the back seam needs to be a sturdy ½", not ¼", and it gives you more 'wiggle' room when seaming. Easy, and professional, instructions are offered by Susan Brubaker Knapp. Best of luck.
http://www.bluemoonriver.com/QuiltSleeve.pdf