Maxwell-Boltzmann Distribution

We are going to start with the answer and work backwards.

$p(E_A)=\dfrac{e^{- \dfrac{E_A}{kt}}}{ \displaystyle \sum e^{-\dfrac{E_A}{kT}}}$

$Z = \displaystyle \sum e^{-\dfrac{E_A}{kT}}$

Z sums over all the probabilities and thus is equal to 1.