Study uncertainty of length propagated from statistics

When we talked about propagated density errors from mass length errors, you mentioned that it will be much simpler if mass lengths obey a Gaussian distribution and it is symmetric. What we were sure is statistics of muon intensity obeys Gaussian, but not so sure about the mass length which is propagated from muon intensity. A check is done now to evaluate the shape of the mass-length distribution from a Gaussian muon intensity distribution. I set the width of the muon intensity Gaussian distribution as 10% (relative uncertainty, which is corresponding 100 muons). For length=200 m, I propagate the mu-intensity distribution (left histogram) to the mass length distribution (right histogram). As you can see, the mass length distribution is close to a Gaussian although it is a bit unsymmetrical. The narrower the width, the closer to a Gaussian. So I think it is safe for you to treat mass lengths obeying Gaussian in calculating density errors. Of course, this is just a check on statistical uncertainty and assume it is our dominating uncertainty.