Question

If the random variable z is the standard normal score and a > 0, is it true that P(z < -a) = P(z > a)? Why or why not?



@ap statistics

Answer 1

True because the normal curve is symmetrical about z=0. If you draw this, the regions are identical.

Answer 2

Is there any work involved in proving it?

Answer 3

Hmmm, my course wasn't too rigorous so that visual proof would have been good enough. If your course is more rigorous you might need to prove it using integrals and the fact that it's even.