The variance of a probability distribution is:

where p is the probability and mu is the mean of the ditribution.
Before we begin we need to find the mean of the distribution, using:

Then the mean is:

hence the mean is 2.52.
Now we can calculate the variance:
![\begin{gathered} \sigma^2=(-50)^2(0.029)+(-30)^2(0.121)+(-10)^2(0.210)+(10)^2(0.485)+(30)^2(0.145)+(50)^2(0.010)-2.52^2 \\ =400.04 \end{gathered}]()
Therefore, the answer is C.