Is my iPhone 5s battery normal?

I had a defective 5s that I bought a week after they came out, the phone died very fast, I visited the Genius Bar twice and the second time he gave me a "new" phone, although it came in a refurbished looking box, not an original new iphone box. It looked new and had a screen protector on the front and back as if it was new, but now that I've had this one for a week I'm questioning that the battery is also bad. Apple acknowledged having a batch of bad iphone 5s; but I don't know if this new (might be refurbished) phone has the same defect.

And please, don't answer by telling me to turn off all of the features that make a smartphone a smartphone, my iphone 4 lasted for an entire day with everything running. (Doesn't really matter because for the last week I've been using my phone with location services off, low brightness, etc.

Thanks in advance!

Added (1). The link is supposed to be a picture it shows that my battery shows 36% yet the about information shows Time Since Last Full Charge:

Usage: 2 hours, 2 minutes.
Standby: 7 hours, 51 minutes.

Added (2). As an update, now (3 hours late than the above) the battery is at 9% and my time says:
Usage: 2 hours, 45 minutes
Standby: 11 hours, 8 minutes

Iphone 5s has a 1560mah and iphone 4 has a 1420mah, it means the 5s should last longer, at least the whole day when used normal.

Your phone has difinetly a battery problem. Tell them to fix it otherwise gate your money back and buy an android phone and say **** off to IOS!