Calculate the standard deviation of X for the probability distribution. Please round your answer to two decimal places, if necessary. $$\begin{array} { | c | c | c | c | c | c | c | }
\hline x & - 5 & - 2 & 0 & 3 & 6 & 10 \
\hline P ( X = x ) & 0.2 & 0.3 & 0.2 & 0.1 & 0 & 0.2 \
\hline
\end{array}$$
A) $\sigma = 10$
B) $\sigma = 13.31$
C) $\sigma = 0.7$
D) $\sigma = 26.61$
E) $\sigma = 5$

Question

Calculate the standard deviation of X for the probability distribution. Please round your answer to two decimal places, if necessary. $$\begin{array} { | c | c | c | c | c | c | c | } 
\hline x & - 5 & - 2 & 0 & 3 & 6 & 10 \
\hline P ( X = x ) & 0.2 & 0.3 & 0.2 & 0.1 & 0 & 0.2 \
\hline
\end{array}$$  
A) $\sigma = 10$
B) $\sigma = 13.31$
C) $\sigma = 0.7$
D) $\sigma = 26.61$
E) $\sigma = 5$

Quizplus · Accepted Answer

To find the standard deviation, first calculate the mean: $\mu = \sum (x \cdot P(X=x)) = (-5)(0.2) + (-2)(0.3) + (0)(0.2) + (3)(0.1) + (6)(0) + (10)(0.2) = -1.1$. Then, calculate the variance: $\sigma^2 = \sum ((x - \mu)^2 \cdot P(X=x)) = 25.41$. Finally, the standard deviation is $\sigma = \sqrt{25.41} \approx 5$.

Calculate the Standard Deviation of X for the Probability Distribution