We analyze the average-case performance of an online scheduling algorithm for independent parallel tasks. We develop a method to calculate an analytical asymptotic average-case performance bound for arbitrary probability distribution of task sizes. In particular, we show that when task sizes are uniformly distributed in the range [1..C], an asymptotic average-case performance bound of {M \over {M - (3 - (1 + {1 \over C})^{C + 1} )C - 1}} can be achieved, where M is the number of processors. We also present extensive numerical and simulation data to demonstrate the accuracy of our analytical bound.