Answer
Here, the variance is:
$(10-21)^2*(.3)+(20-21)^2*(.4)+(30-21)^2*(.2)+(40-21)^2*(.1)=89$
The standard deviation is the square root of the variance:
The standard deviation here equals to $\sqrt{89}=9.43$
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: $(.3)*10+(.4)*20+(.2)*30+(.1)*40=21$
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:
$(10-21)^2*(.3)+(20-21)^2*(.4)+(30-21)^2*(.2)+(40-21)^2*(.1)=89$
The standard deviation is the square root of the variance:
The standard deviation here equals to $\sqrt{89}=9.43$
