I currently have a Samsung Galaxy S4, so my thought will be general.
With the S4, I can adjust the ringer using the volume control. The choices are silent, vibrate and audio.
Also, I can customize notification for each individual telephone number in my directory.
I'm fairly sure that the iPhone has a similar arrangement. My guess is that...if all incoming calls result in vibration...check the volume control to see if it is set to vibrate only. On the S4, that would be the picture of a speaker with a line struck through it and wavey brackets on the left and right sides of the speaker image itself.
The iPhone ccan be muted in 3 ways, 4 if your default ringtone is set to 'none'.
IS do not disturb on? Swipe control center up and turn the moon icon off
if the side switch set to off? Near the volume buttons is a small switch, if you can see red, it is turned off.
the other way is the volume is all the way down and the phone will only vibrate.