A good rule of thumb, is whenever you purchase a new rechargeable battery, for the first 3 times, you should charge and discharge the battery fully (aka don't charge the battery until it is nearly dead, and give it a full charge). Most batteries these days don't have a 'memory', but its still good practice to fully cycle the chemicals within. Just in general, with rechargeable batteries, since they rely on reversing the chemical reaction within, when you consistently 'don't use' a portion of it, it has the possibility to build a hardened layer at that point, which effectively shrinks your battery life to that point. This is the case with a bit older batteries, although i do not know if newer batteries function this way (i'd imagine so; battery technology hasn't made too much progress in the last 10 years; and even if they have developed new stuff, it takes time for those technologies to hit the general consumer market).
That being said, i don't think there is a problem with your battery. I am linking a thread that also discussed battery life of the phone, and in there i added a post regarding how batteries recharge (post #5 or so), if you know a bit about the science behind them.
What i would suggest, charge it full, and then use it completely, and then note how long the battery lasts. If it is reasonable (2-3 days, more or less depending on usage), then i wouldn't worry about it. in rehash of the post i made in the link, it will take about 1 hour to charge the phone 80-90%, but will take ~5 hours to give it a full charge (with the first time perhaps taking a bit longer; at least i know mine did).
Again, i suggest charging most of your devices full, and then not charging them till they're nearly dead in general, sure here and there it is fine to recharge however it fits your time constraints or needs, but once in a while, give it a full charge and discharge. Unlike laptop batteries, where it is completely normal to never discharge it fully and it doesn't really damage anything, most smaller devices have hte possibility of damaging hte battery. That is because they generally have 1 battery cell (or only a few), whereas laptop batteries and other larger batteries have multiple smaller cells. Think of it where if that one cell has chemical hardening occur in it, and caps the battery life at 70%, then overall it has 70% life. With the multiple cells, say you use the laptop to at max, 50%. Then half of the cells retain 100% power, and the other half chemically digresses to 70%. That means you have 85% battery capacity. But, simple technology would make it so the laptop battery cycles through its cells, moving some of the 'lower' cells to be used first, and then vice versa at other times, which would fully discharge and charge every small cell, resulting in no capacity loss. A single cell doesn't have the capability to cycle cells like this..cause there is only 1. Note that i do not know if this is how the multiple-cell batteries actually work, but even if i'm wrong, the point is the same: they are designed differently, and having only 1 cell limits the possibilities of designing out basic chemical properties that can lead to reduced performance.
See how many emails you have set to be synced on your phone. We found a big difference in the amount of drain on the battery by setting that to a day or two instead of having a ton of emails on the phone.