So the standard deviation-- maybe I'll draw it this way.

所以标准偏差——也许我会这样画。

It has a standard deviation of 0.7 liters or 0.7 liters.

它的标准偏差为 0.7 升或 0.7 升。

And then one standard deviation is going to be 0.7 liters away.

然后一个标准偏差将是 0.7 升。

Remember, z-score is just how many standard deviations you are away from the mean.

请记住，z-score 就是您与平均值之间的标准偏差数。

So what we're going to do is estimate it with our sample standard deviation.

所以我们要做的是用我们的样本标准偏差来估它。

And we know that the standard deviation is equal to-- I'll write the 0 in front, 0.7 liters.

我们知道标准偏差等于——我会在前面写上 0，即 0.7 升。

That's going to be the standard deviation of this.

这将是这个的标准偏差。

And that equaled 1 over the standard deviation.

这等于标准偏差的 1。

So in this situation the standard deviation is the square root of 25.

所以在这种情况下，标准偏差是 25 的平方根。

So I say the probability of 45 left moves is equal to 1 over the standard deviation.

所以我说 45 次向左移动的概率等于标准偏差的 1。

It's going to have a lower standard deviation.

它将具有较低的标准偏差。

The standard deviation of this distribution is 0.099.

此分布的标准偏差为 0.099。

This is actually going to be a normal distribution regardless of-- this one just has a well-defined standard deviation mean.

这实际上将是一个正态分布，无论如何 - 这个只是有一个明确定义的标准偏差平均值。

If you take more samples than our estimate of the standard deviation of this distribution will go down because this denominator will be higher.

如果您抽取的样本数量多于我们对该分布的标准偏差的估值，那么该分布的标准偏差将会下降，因为该分母会更高。

Where the standard deviation right now is almost 0.1, so it's 0.09, almost a tenth.

现在的标准偏差几乎是 0.1，所以它是 0.09，几乎是十分之一。

And the standard deviation is 0.5.

标准偏差为 0.5。

And if you wanted the standard deviation of this distribution right here, you just take the square root of both sides.

如果你想要这个分布的标准偏差就在这里，你只需取两边的平方根。

But even a more interesting thing is our standard deviation is smaller.

但更有趣的是我们的标准偏差更小。

So the mean is five, 2 minus five divided by the standard deviation, divided by 1.581, all of that squared.

所以平均值是 5， 2 减去 5 除以标准偏差，再除以 1. 581，所有结果的平方。

And the standard deviation of these 10 data points right here is 2.98, the sample standard deviation.

这 10 个数据点的标准偏差为 2.98，即样本标准偏差。