# Bounds for samples from the normal distribution using numpy.random.randn

I am new to both stats and scientific Python, so apologies if this question breaches any guidelines.

I want to know what x = np.random.randn(500) actually does, in terms I can understand. Why exactly does plotting x give values in the range shown in this image:

?

It looks like the values range roughly from -3 to 3, yet I can find no mention of the range in documentation for numpy.random.randn. Therefore I'm assuming this property must somehow be intrinsic to a standard normal distribution, but I don't have enough knowledge of this entity to understand why.

Is it possible, although wildly improbable, that values with a much greater magnitude could be generated? Is it a feature of the specific implementation that the values range from -3 to +3 ish, rather than, say, -10 to +10 ish?

• randn simply generates pseudo-random numbers from the standard normal distribution (en.wikipedia.org/wiki/…). The values are unbound, but very large and very small values are highly improbable. Commented Jan 25, 2021 at 15:37

• No: by definition, the variance is $1.$