A note on the reasonableness of PERT hypotheses

In this paper the expression for the mean in the PERT method is considered. This mean involves a parameter k, that sometimes has been set to 4. Insisting on the similarity between the beta and the normal distributions, certain hypotheses are proposed that lead to k necessarily being exactly 4. More specifically, but using the moments of the second and fourth orders, it is shown that the usual beta distribution in the PERT method is mesokurtic (γ=3) and of constant variance (σ² = 1/36).