The results of a study showed that heterosexual women, during ovulation, were significantly better at correctly identifying the sexual orientation of a man from a photograph of his face than women who were not ovulating. Near ovulation, on average women correctly identified the orientation of about $67\%$ of the $100$ men shown to them. Assume that the sample distribution for this study is unimodal and symmetric an a that the samples are collected randomly. If this is the probability of correctly identifying the orientation of a man in any given photograph, what is the probability a woman would correctly classify $79$ or more of the men?