[Script Info]
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[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.27,0:00:04.49,Default,,0000,0000,0000,,Now remember, when we calculate the z score of any value in the distribution,
Dialogue: 0,0:00:04.49,0:00:08.85,Default,,0000,0000,0000,,we first subtract the mean which shifts the distribution without changing the
Dialogue: 0,0:00:08.85,0:00:15.29,Default,,0000,0000,0000,,shape so that zero is now the mean. And when we divide by the standard
Dialogue: 0,0:00:15.29,0:00:21.20,Default,,0000,0000,0000,,deviation, we then change the shape. Let's look at it this way. We have any
Dialogue: 0,0:00:21.20,0:00:26.77,Default,,0000,0000,0000,,distribution, with mean, mu, and standard deviation, sigma. Which basically
Dialogue: 0,0:00:26.77,0:00:30.71,Default,,0000,0000,0000,,means that sigma is one standard deviation away from the mean. After we
Dialogue: 0,0:00:30.71,0:00:36.40,Default,,0000,0000,0000,,standardize this distribution, what is going to be the z-score of sigma? Well,
Dialogue: 0,0:00:36.40,0:00:42.96,Default,,0000,0000,0000,,remember when we subtract mu, we shift it so that mu is now zero. So now, the
Dialogue: 0,0:00:42.96,0:00:48.15,Default,,0000,0000,0000,,z-score of sigma is going to be sigma minus zero divided by sigma, which is
Dialogue: 0,0:00:48.15,0:00:55.29,Default,,0000,0000,0000,,sigma divided by sigma, which is 1. So, the z-score of any value, that's one
Dialogue: 0,0:00:55.29,0:01:02.70,Default,,0000,0000,0000,,standard deviation away from the mean, will then be 1 after we standardize it.
Dialogue: 0,0:01:02.70,0:01:07.24,Default,,0000,0000,0000,,Which means that the new standard deviation of this normalized distribution, or
Dialogue: 0,0:01:07.24,0:01:10.38,Default,,0000,0000,0000,,standard distribution, is 1.