How old is the Laptop? If it is still under warranty, they will likely replace the battery for you. But to answer your question, no, it is not normal to only be able to get a 50% charge. On my HP DV6, when the battery went bad, it just wouldn't hold a charge for long. When it was plugged in, it would get up to 100%. A quick search on the good ole www, resulted in quite a few circumstances where people are experiencing the same issue. It seems maybe you did not follow the manufacturers "New battery charging instructions".
Try this, leave the laptop unplugged and watch a movie, or something that will drain the battery fast. Let it die completely and then recharge it for 12 hours and see what happens.
Let us know.