For any continous variable and indeed for \(\overline{X}\text{,}\) \(P(\overline{X} = \mu) = 0\text{.}\) In general, you should expect a sample statistic to be close but not precisely equal to the population statistic. Indeed, if you were so lucky as to have the sample statistic to land on the population statistic, doing one more trial would mess things up anyway and the sample statistic would certainly change some.