1. Let's start by understanding what a z-score represents. A z-score measures how many standard deviations a data point is from the mean of a distribution. 2. The 10th percentile means the value below which 10% of the data falls. Since the normal distribution is symmetric around the mean, the 10th percentile is to the left of the mean. 3. Because the mean corresponds to a z-score of 0, any value to the left (less than the mean) will have a negative z-score. 4. Therefore, the z-score for the 10th percentile is negative because it represents a value below the mean, specifically about $$z \approx -1.28$$ for the standard normal distribution. 5. In summary, the negative sign indicates the position of the 10th percentile is below the mean on the distribution curve.