Answer
Here, the variance is:
$(-20-(-4))^2*(.2)+(-10-(-4))^2*(.4)+(0-(-4))^2*(.2)+(10-(-4))^2*(.1)+(20-(-4))^2*0+(30-(-4))^2*(.1)=204$
The standard deviation is the square root of the variance:
The standard deviation here equals to $\sqrt{204}=14.28$
Work Step by Step
In order to calculate the standard deviation, we have to get the expected value of the probability distribution.
Here, we can calculate it as:
$p_{1}\times X_1+p_2 \times X_2 +...$
Where $p$ is the probability, $X$ is the value for every possible value of the distribution.
The expected value is: $(.2)*-20+(.4)*-10+(.2)*0+(.1)*10+(.0)*20+(.1)*30=-4$
The variance of X can be calculated as:
$(X_1-E(X))^2*p_1+(X_2-E(X))^2*p_2+...$
Here, the variance is:
$(-20-(-4))^2*(.2)+(-10-(-4))^2*(.4)+(0-(-4))^2*(.2)+(10-(-4))^2*(.1)+(20-(-4))^2*0+(30-(-4))^2*(.1)=204$
The standard deviation is the square root of the variance:
The standard deviation here equals to $\sqrt{204}=14.28$