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?
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 $1/2$.
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