Boltzmann factor question

Heya, just another panicking sixth form student question here...
My textbook says particles have random thermal energy of the order of 'kT' where k is the Boltzmann constant; 3/2 kT is apparently the average kinetic energy of particles at a certain temperature. I'd assumed this mean that when activation energy 'E'=kT, pretty much all of the particles (or at least the majority of them) were able to take part in the reaction, because on average, they all have the necessary energy (more in fact, if the kinetic energy IS 3/2 kT). However, the Boltzmann factor exp.(-E/kT) suggests that when the average kinetic energy is of the order of magnitude of the activation energy, only exp.(-1), or 1/e (about 0.37) of the particles are in the higher state/able to take part in the reaction. I get how the Boltzmann factor is derived, I'm just not sure about the conclusions to draw from it- does it contradict what the book previously explained?

Thanks, any responses appreciated.