Many human traits, like height, follow a normal distribution.

许多人类特质，例如身高，就符合常态分布。

In statistics, a normal distribution describes a set of values that fall along a bell curve.

在统计学中，常态分布的意思是呈现钟形分布的一系列值。

This is a depiction of what we used to think of as the normal distribution of temperatures.

这是我们之前使用的温度常态分布图。

So this is going to be a normal distribution.

所以这将是一个正态分布。

So this distribution, once again, we don't know whether it's a normal distribution or not.

所以这个分布，再一次，我们不知道它是否是正态分布。

And we know that that is going to be a normal distribution.

我们知道这将是正态分布。

And we know a few of the properties of that normal distribution.

我们知道正态分布的一些特性。

His name also graces the Gaussian distribution, also known as the normal distribution or bell curve, a fundamental tool in the natural and social sciences.

他的名字也为高斯分布增光添彩，高斯分布也称为正态分布或钟形曲线，是自然科学和社会科学的基本工具。

But then, it still would be difficult for it to become an exact normal distribution.

但是那样的话，它仍然很难成为一个精确的正态分布。

So it still won't be a normal distribution when n is equal to 2.

所以当 n 等于 2 时，它仍然不是正态分布。

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。

We're going to get some normal distribution.

我们将获得一些正态分布。

This is clearly not a normal distribution.

这显然不是正态分布。

So this converges to a normal distribution very quickly.

所以这很快收敛到正态分布。

At some point, it might look a lot like a normal distribution.

在某些时候，它可能看起来很像正态分布。

The central limit theorem says as n approaches, really as it approaches infinity, then is when you get the real normal distribution.

中心极限定理说当 n 接近时，实际上当它接近无穷大时，就是当你得到真正的正态分布时。

If you get to n equals 10 or n equals 15, you're getting very close to a normal distribution.

如果你得到 n 等于 10 或 n 等于 15，你就会非常接近正态分布。

These are both pretty good approximations of normal distributions.

这些都是正态分布的很好的近似值。

So as that approaches infinity, your actual sampling distribution of the sample mean will approach a normal distribution.

因此，当它接近无穷大时，样本均值的实际抽样分布将接近正态分布。

And then it has a negative kurtosis, which means that it has shorter tails and smaller peaks than a standard normal distribution.

然后它有一个负峰度，这意味着它比标准正态分布有更短的尾巴和更小的峰。