General characteristics of a normal distribution If the normal distribution curve is symmetrical about the vertical line then the 
mean = mode = median 
This would mean that:
Prob( X < mean) = Prob( X > mean) = .....  

What is the missing part of this concept?

Generally for continuous probability distributions that are symmetric about their median, if they have a mean at all, then the probability of being greater than the mean and the probability of being less than the mean are both equal to $1/2$.
