Using the exact weightings for the muon multiplicity distributions as described below, I made a plot of the change in the number of background events with respect to variations in the tag and fake rates.

Variations in the muon tag rate have more of a systematic effect on the background estimate than corresponding variations in the pion/kaon/proton mistag rates. In addition, the change in the number of background events is linear with respect to tag rate variations in all cases.

Next I take the 10% variations of both the real and fake rates and run a Bayesian limit calculator using 1000 pseudoexperiments drawn from the null hypothesis. We ask for 95% credibility level. The program returns the scale factor on the signal model that is excluded at this level. The output is as follows:

Observed : 0.305
Expected : mean=0.284 +1sig=0.396 -1sig=0.222 +2sig=0.589 -2sig=0.185

The observed exclusion is slightly stronger than expected, but completely within the 1 sigma bands. The signal model is excluded at 95% credibility at a cross-section of 30% of that provided.