In Statistics, when you are is using the standard normal distribution, P(z < 0) = 0.5.
A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which shows that all data near the mean have a higher frequency than data that are far from the mean.
This ultimately implies that, when you are is using the standard normal distribution, P(z < 0) must be equal to 0.5 because it has a median of zero (0).
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