For a Gaussian distribution of the (J − K) colours at the TRGB with a width of 0.05 mag, and the relation between M_K and (J − K) discussed in the text, the black histogram is the theoretical distribution of the K-mag of stars at the TRGB for a Galaxy at the distance of the LMC. Since the LF is sampled, the actual distribution of all RGB stars in K is the blue histogram. The cut-off is not sharp and samples neither the true brightest RGB stars, nor the peak in the true K-mag distribution. The red histogram shows the simulated distribution in T-mag (shifted by −2.013 <  SPSDOUBLEDOLLAR >  × the adopted mean (J − K) colour at the TRGB). The cut-off is much sharper.