What is Boltzmann distribution, population?

Example 10.8 (The rotational levels of hydrogen chloride)

For $\ce{H^{35}Cl}$, $B_0 = B_e - \alpha_e/2 = 10.44\,\mathrm{cm}^{-1}$. At $300\,\mathrm{K}$ the level $J$ lies at $10.44\,J(J+1)$ $\mathrm{cm}^{-1}$, i.e. $0.0501\,J(J+1)$ in units of $kT$. The terms $(2J+1)\eu^{-0.0501J(J+1)}$ are 1, 2.71, 3.70, 3.84, 3.31, 2.45, …; their sum is $q = 20.3$ and the populations of $J = 0$ to 4 are 0.049, 0.134, 0.182, 0.189 and 0.163: the most populated level is $J = 3$, not $J = 0$, because the degeneracy $2J + 1$ grows while the Boltzmann factor falls. This is the envelope of the rotation–vibration band of Chapter 6.