Optional Topic: Cumulative Normal Distribution Function

Graphs of the cumulative normal distribution function used to be seen much more frequently than they are today. The cumulative function gives the probability that a random value will be equal to or less than the specified value. For example, from working with the previous graphs, we know that the probability that a z-score will be less than or equal to 0 is .5. The graph of the cumulative normal distribution function associates the cumulative probability with each z-score.

These graphs allow you to explore the relationship between the normal density function and the cumulative distribution.

Quantiles and Percentiles

The f quantile (or the 100 x f percentile) is the score that is equal to or greater than proportion f (or 100 x f%) of the observations. For example, the .5 quantile (or 50th percentile) z-score equals 0 because 0 is greater than or equal to .5 (or 50 percent) of all z-scores. Use the left graph above to find other quantiles (approximately, due to screen resolution). Select any score along the horizontal axis and then read the corresponding quantile along the vertical axis. Or alternatively, drag along the horizontal axis until the desired quantile is shown.