Final answer:
A z-table value for the area under the standard normal curve that is less than 0.5 will have a negative z-score, indicating that the corresponding percentile is below the median of the distribution.
Step-by-step explanation:
A z-table value representing the area under the standard normal curve that is less than 0.5 corresponds to a z-score that is below the mean. This is because the standard normal distribution is symmetrical around the mean of zero, and an area of less than 0.5 indicates that we are looking for a score that lies to the left of the mean.
Therefore, if the z-table value for the area under the standard normal curve is less than 0.5, the z-score will be negative. This means that the corresponding data point falls below the mean of the distribution. The percentile corresponding to this area will be less than the 50th percentile, which represents the median.
To clarify, a z-score of zero represents the mean of the distribution, and areas to the left of this point are less than 0.5. Areas to the right are greater than 0.5 and correspond to positive z-scores. In conclusion, a z-table value for the area under the standard normal curve that is less than 0.5 will have a negative z-score.