In a Normal distribution, the z-score with approximately 50% of observations below it is 0. This z-score represents the mean of the distribution, equivalently, the median or 50th percentile.
In a Normal model, the z-score expected to have approximately 50% of observations below it is 0. The Normal distribution is symmetric around its mean, and a z-score of 0 represents the mean of the distribution. Since 50% of the observations lie to the left of the mean in a Normal distribution, a z-score of 0 corresponds to the median, or the 50th percentile.
About 68% of the values lie between z-scores of -1 and 1, while approximately 95% lie between z-scores of -2 and 2. This is according to the empirical rule which is also known as the 68-95-99.7 rule. By definition, a z-score provides the number of standard deviations a value (x) is from the mean (µ) of a normally distributed variable. Since a standard normal distribution has a mean of 0 and a standard deviation of 1, the requested z-score for this context is z=0.