There is actually some good research on this from Pew, Gallup and others. I would check it out by searching at their sites. However, here are some examples:
General overview of Muslim beliefs around the globe: Pew report on Muslim world paints a distressing picture
Interestingly, among all religions polled in the U.S., Muslims were the LEAST likely to support violence. See Most Muslim Americans See No Justification for Violence
Here is a good overview of research on Muslim attitudes towards terrorism:
Muslim attitudes toward terrorism
And here is a more complex overview of attitudes of tolerance and what contributes to them: Views of Violence
My 2 cents.
(From Quora question: https://www.quora.com/Do-moderate-Muslims-really-support-terrorist-acts-by-radical-Muslims-as-right-wing-conservatives-claim)
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