Final answer:
Transforming a distribution to z-scores results in a new distribution called the standard normal distribution, with a mean of zero and a standard deviation of one. Z-scores standardize values from different distributions for comparability.
Step-by-step explanation:
Transforming all the values in a distribution to z-scores gives the distribution a mean of zero and a standard deviation of one. A z-score is a standardized value that reflects how many standard deviations a value is from the mean of the distribution. When applied to a distribution, z-scores create the standard normal distribution, commonly denoted as Z ~ N(0, 1). Such a transformation allows for comparison between different datasets by standardizing them. The formula for calculating a z-score is z = (x - μ) / σ, where x is a value from the original distribution, μ is the mean, and σ is the standard deviation of that distribution.