text: Is 3 the standard deviation or the variance?  Since X1, X2, and X3 are all nromal and independent, then \n\nX1 + X2 + X3 ~ N(0+0+0 = 0, sqrt(3^2+3^2+3^2) = sqrt(27)), if 3 was the SD.\nN(0, 3+3+3 = 9) if 3 was the variance.\n\nIn general, if X_i ~ N(mu_i, sigma_i), where sigma_i is the SD, then the sum of X_i ~ N(sum mu_i, sqrt(sum (sigma_i)^2)).\n\nSince the mean of your distribution is 0, then P(X1+X2+X3>0) = 0.5.  Remember that the mean splits the normal distribution in half.