Final answer:
The correct answer to the question is D. An observation with a z-score of 0 means that the observation is equal to the mean of the data set.
Step-by-step explanation:
If an observation has a z-score of 0, this means the observation is equal to the mean of the dataset. When we talk about z-scores in the context of a standard normal distribution, which is denoted as Z ~ N(0, 1), it represents a distribution with a mean of 0 and a standard deviation of 1.
Therefore, a z-score of 0 simply indicates that the observation is right at the mean of the dataset. This is because the z-score measures the number of standard deviations an individual observation is from the mean. Positive z-scores indicate values above the mean, while negative z-scores indicate values below the mean.
Considering this, the correct answer to the student's questions A, B, C, and D is D. The observation is equal to the mean. Other options can be dismissed: A is incorrect because a z-score does not equate to the standard deviation directly; B is incorrect because the median is not necessarily equal to the mean, and C is incorrect because a z-score of 0 is a possible and correct calculation.