Final answer:
A z-score of -3 corresponds to the 0.15th percentile, but rounded to the nearest tenth of a percent, it is approximately the 0.2 percentile in a normal distribution.
Step-by-step explanation:
To determine what percentile a z-score of -3 is, we need to refer to the empirical rule, which is also known as the 68-95-99.7 rule. This rule states that roughly 68 percent of values will fall between z-scores of -1 and 1, about 95 percent of values will fall between z-scores of -2 and 2, and about 99.7 percent of values will lie between z-scores of -3 and 3 in a normal distribution.
Given that the z-score of -3 is at the extreme end of this distribution, we can infer that a z-score of -3 corresponds to the lowest 0.15 percent of values (100% - 99.7% / 2 = 0.15%), as the data is symmetrically distributed. So, z = -3 approximately corresponds to the 0.15th percentile when the data is normally distributed.
Thus, the answer rounded to the nearest tenth of a percent is that z = -3 corresponds to the 0.2 percentile.