[sbayless]

Hmm, I don't actually think chebyshev applies (in a meaningful way) in this context. 3.5 sigmas refers to the probability of the observation being significant, not the average mass of the higgs. Or did I misunderstand what you meant?

As an aside, there is a typo in the parent's link: http://en.wikipedia.org/wiki/Chebyshev_inequality

[tel]

3.5 sigmas refers to the probability of some statistic being as severe as they're observing under a model where the Higgs does not exist. Regardless of the distribution, Chebyshev applies solely by assumption that sigma is a meaningful unit. It may be overly conservative though.

[orijing]

Thanks for the correction. That link worked when I checked...

Well, Chebyshev inequality always applies. It just might not be the tightest bound possible. Unless we know the distribution better, this is the best estimate (tightest bound that's provably correct given the single assumption about standard deviation)