A note about z-scores: All z-scores do not follow a Normal distribution. A z-score simply tells how many standard deviations a value is from the mean, no matter what the shape of the distribution. The distribution of z-scores should have the same shape as the original distribution, but with a mean of 0 and a standard deviation of 1. When comparing z-scores from different distributions, it is important that the distributions be roughly the same shape. A z-score of +2 is very unusual in a uniform distribution, but not that uncommon in a distribution strongly skewed to the right.

A note about notation: In general, we will use Greek letters to represent the “true” value of a numerical summary, such as the mean, and non-Greek letters to represent the estimated value of the numerical summary. A note about Normal Probability Plots: NPPs are not tested on the AP Exam.