The black curve shown below is the density function
of the T distribution with df degrees of freedom.
By moving the scroll bar you can change the degrees of freedom.
The red curve is the density function of the standard normal distribution.
The blue vertical line (which appeares for df greater then 2) shows the
interval (-σ,σ). Thus,
its length is twice the standard deviation (σ) of
the T distribution with df degrees of freedom. Note that for a
degrees of freedom of 1 or 2
the standard deviation of the T distribution is infinite.