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?

Since

Prob(X < mean) + Prob (X = mean) + Prob (X > mean)=1
and Prob(X = mean)=0   (continuous distribution)

You get

Prob(X < mean) = Prob (X > mean)=0.5

