Walking through the 68-95-99.7 rule with integral explanation of its source.

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Some images made using Geogebra.

0:00 What does the empirical rule tell us?
1:05 Normal Distribution probability density function.
1:45 Normal curve with mean of 0 and standard deviation of 1.
2:20 Probability at point vs probability of interval.
2:52 Using integral to calculate area under normal curve.
3:11 Integrals to compute area between standard deviation of the mean for N(0,1) example.
4:29 Setting up table to compare areas for different normal curves.
5:01 How does changing the standard deviation change the spread of the curve?
5:40 Integrals to compute area between standard deviation of the mean for N(0,0.5) example.
6:35 Integrals to compute area between standard deviation of the mean for N(50,10) example.
7:30 Integrals to compute area between standard deviation of the mean for N(1000,25) example.
7:45 Conversation about how area under curve didn't change when varying the mean and standard deviation.
8:12 The empirical rule saves you time from recalculating integrals over and over again.

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