Final answer:
Approximately 68% of students' scores are expected to be within one standard deviation from the mean in a normal distribution, which is between 51 and 64 for the given data.
Step-by-step explanation:
The scores of eighth-grade students in a math test are normally distributed with a mean of 57.5 and a standard deviation of 6.5. From this data, we can conclude that approximately 68% of the students' scores will fall within one standard deviation of the mean. This means that 68% of the students' scores are likely to be between 51 (57.5 - 6.5) and 64 (57.5 + 6.5). This is known as the empirical rule or the 68-95-99.7 rule, which states that in a normal distribution, about 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.