Normalised cumulative distribution of the observed single MBHs (blue histogram) and of our mock MBHBs (red histrogram). The solid black line shows the median cumulative probability that a system will have a of lower than a given value (obtained from the single MBH data under the assumptions specified in the main text). The teal band indicates the 90% credible region for the cumulative distribution of for single MBHs. The vertical red (blue) ticks highlight the values for all of the 36 mock binaries (9 single MBHs). The numerical values of all of the and cumulative probabilities are listed in Table 1.