Question

b. A normal distribution is by definition symmetrical. What does such symmetry mean from a probability standpoint?

Answer 1

Suppose that X follows Normal distribution with mean and standard deviation sigma

Then ~ N(0,1)

I.e Z ~ N(0,1)

Now symmetry means probability less than zero and greater than zero both are equal & which are equal to = 0.5

That is data symmetrical divided on both sides of zero.

Due to symmetry In terms of probability we also say that,

and both are equal.

and both are equal.