If I have only maximum and minimum values, can I calculate mean value of normal distribution?
The distribution itself doesn't have a max and min. Presumably you have a sample from the distribution. The best you can do is take the mean of the max and min. But this will be sensitive to variation in the max and min of your sample, which is much worse than (say) the median of your sample. You can prove that the mean of your sample is an unbiased estimator of the mean of the distribution with less variance than the distribution itself.