In the standard normal distribution, P(Z ≤ 0) is equal to: | Agrigyan

Symmetry of the standard normal distribution:

• Total probability under the entire normal curve from $-\infty$ to $+\infty$ is $1$.
• The standard normal distribution curve is symmetric around its mean $\mu = 0$. Therefore, exactly half of the total probability lies to the left of the mean, making $P(Z \le 0) = 0.5$.
• While $0.5 \gt 0$, the exact numerical value is $0.5$.
• While $0.5 \lt 1$, the exact numerical value is $0.5$.