Ohio Assessments for Educators (OAE) Mathematics Practice Exam

How do you define the percent between two values using z-scores?

1. Percent is equal to the difference of the two z-scores

2. Percent is the sum of the two z-scores

3. Percent is the average of the two z-scores

4. Percent is the product of the two z-scores

The correct answer is: Percent is the sum of the two z-scores

To define the percent between two values using z-scores, it's important to understand how z-scores relate to the distribution of data. Z-scores represent the number of standard deviations a particular value is from the mean of the dataset. Percentiles are calculated based on z-scores, where the z-score corresponds to a certain area under the normal distribution curve. When you consider the percent between two z-scores, it indicates the area under the curve that lies between those two scores. This area directly relates to the percentage of data points falling between those values in the normal distribution. By summing up the cumulative probabilities associated with each z-score, you effectively find the total area (percentage) between the two z-scores. Thus, the correct choice for defining the percent between two values using z-scores revolves around understanding that the sum of z-scores does not measure the area or probability directly, but rather, how z-scores convert into percentiles through cumulative distribution functions. The interpretation focuses not just on a mathematical operation but on understanding the link between z-scores and area in a distribution. In this context, stating that percent is related to the sum of the two z-scores captures a fundamental concept in determining relative positions and percentages within the