The Maxwell-Boltzmann distribution curves for a given reaction mixture at two different temperatures, $T_1$ and $T_2$, are shown below, along with the activation energies for the catalysed ($E_{cat}$) and uncatalysed ($E_a$) pathways.

Which statement(s) is/are correct?

1. The average kinetic energy of the molecules is greater at $T_2$ than at $T_1$.
2. The total area under the curve at $T_2$ is greater than that at $T_1$ because the molecules possess more thermal energy.
3. At temperature $T_1$, the number of molecules with energy greater than or equal to the activation energy increases from the area under the curve to the right of $E_a$ to the area under the curve to the right of $E_{cat}$ when a catalyst is used.