When a fair coin is tossed [i][math]n[/math][/i] times, the probability bar graph can be displayed in the interactive figure, where [i][math]n[/math][/i] can be varied with the slider. The probability of getting between [i][math]c[/math][/i] and [i][math]d[/math][/i] (inclusively) successes is[br][br][center] [math]P\left(c\le X\le d\right)=\sum_c^dP\left(X\right)[/math][br][/center]When working with a continuous random variable that is a probability density function [i][math]f[/math][/i], the probability of getting between [i][math]c[/math][/i] and [i][math]d[/math][/i] successes is[br][br][center][math]P\left(c\le X\le d\right)=\int_c^df\left(X\right)dX[/math][/center]This can also be demonstrated in the interactive figure. When the continuous normal distribution model is shown, you can vary [i][math]c[/math][/i] and [i][math]d[/math][/i] by moving the points on the [i][math]x[/math][/i]-axis.[br][br]

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]