What is a basic assumption of a z-score?

A z-score standardizes a value by expressing how many standard deviations it lies from the mean. A fundamental assumption of z-score analysis in data-driven decision making is that the data can be transformed to a standard normal distribution with a mean of zero and a standard deviation of one.

This transformation allows analysts to compare values from different distributions on a common scale and to calculate probabilities using the standard normal table. The formula for a z-score subtracts the mean from the observed value and divides by the standard deviation, resulting in this standardized distribution.

Outliers are not eliminated by default in z-score calculations; instead, z-scores are often used to identify outliers. A standard deviation of 2 is incorrect and would not represent a standardized distribution.

Therefore, the correct answer is A, reflecting the core assumption underlying z-score usage.