Final answer:
The z-score for a data value 3 standard deviations to the left of the mean is -3, indicating it is significantly below the mean, specifically in the left tail of the distribution.
Step-by-step explanation:
The z-score of a data value that is 3 standard deviations to the left of the mean is -3. The z-score represents how many standard deviations an observation or data point is from the mean of the data set. If a data value is to the left of the mean, this indicates that it is less than the mean, which results in a negative z-score.
In the context of the standard normal distribution, which has a mean of 0 and a standard deviation of 1, a data value that is 3 standard deviations to the left would have a z-score of -3. According to the empirical rule, about 99.7% of the values lie within three standard deviations of the mean, thus a z-score of -3 is quite far from the mean in the left tail of the distribution.