We showed in [2] that if r≤2, zero mean Gaussian of average error of the Trapezoidal rule is proportional to h_i^2r+3 on the interval [0,1]. In this paper, if r≥3, we show that zero mean Gaussian of average error of the Trapezoidal rule is bounded by Ch⁴_ih⁴_j. AMS Mathematics Subject Classification : 65D30, 65G10, 28C20