Can a negative z score be greater than a positive z score?

Assume the z-score is relative to zero score. In simple terms, assume that we have 0 < z < z0, where z0 is the arbitrary value.

Then, a negative z-score can be greater than a positive z-score (yes). How? Determine the probability of P(-2 < z < 0) and P(0 < z < 1). Then, by checking the z-value table, you should get:

P(-2 < z < 0) ≈ 0.47725

P(0 < z < 1) ≈ 0.341345