Is this usually how fast a smartphone battery drains?

[Casper]

It would depend on what you have enabled such as wifi, 3G(or 4G), brightness allowed, (if possible) push and fetch for mail, what applications are running in the background, and how long you've had it.

You can make your battery last longer by using yor cellular network and data only when you need it, or using wifi where given, charging it to full when it's almost (almost!) completely drained, such as, around 20% and such. Setting mail options to fetch manually (if your device supports fetch and push) turning off bluetooth, and dimming your screen to an acceptable level.