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Assume that we have N independent observations from a continuous distribution with known median, assumed zero without any loss of generality. We want to test whether the distribution is symmetric about zero. Vaious tests are proposed in the literature for this hypothesis. Baklizi (2007) introduced a test based on a trimmed longest run statistic in asuitably defined sequence of Bernoulli trials. The test was shown by simulation to have a performance at least about that of its competitors. However, the distribution of this test statistic does not have a simple closed form. In this paper we shall consider various approximations of the tail areas of this test statistic and compare their performance