Answer
Here, the variance is:
$(2-4.5)^2*(.05)+(4-4.5)^2*(.75)+(6-4.5)^2*(.1)+(8-4.5)^2*(.1)=1.95$
The standard deviation is the square root of the variance:
The standard deviation here equals to $\sqrt{1.95}=1.4$
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: $(.05)*2+(.75)*4+(.1)*6+(.1)*8=4.5$
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:
$(2-4.5)^2*(.05)+(4-4.5)^2*(.75)+(6-4.5)^2*(.1)+(8-4.5)^2*(.1)=1.95$
The standard deviation is the square root of the variance:
The standard deviation here equals to $\sqrt{1.95}=1.4$
