AP statistics chapter 6 Stats modeling the world third edition by David E. Bock

The chapter introduces us to normal models, which are commonly used to display percentiles, for example: SAT scores, household incomes, and many other things. In order to express the distance in standard deviations standardizes the performances.To standardize a value, we simply subtract the mean performance in that event and then divide this difference by the standard deviation; this is called Z scores. In order to see the percentile display by the Z score, we need to use a formula chart.

Z score is (X - mean)/standard deviation