The probability model below describes the number of thunderstorms that a certain town may experience during the month of August. $$\begin{array} { l | c c c c }
\text { Number of storms } & 0 & 1 & 2 & 3 \
\hline \text { Probability } & 0.1 & 0.2 & 0.4 & 0.3
\end{array}$$ What is the standard deviation of the number of storms in August?
A)0.88
B)0.94
C)0.66
D)0.75
E)0.77

Question

The probability model below describes the number of thunderstorms that a certain town may experience during the month of August. $$\begin{array} { l | c c c c } 
\text { Number of storms } & 0 & 1 & 2 & 3 \
\hline \text { Probability } & 0.1 & 0.2 & 0.4 & 0.3
\end{array}$$ What is the standard deviation of the number of storms in August?
A)0.88
B)0.94
C)0.66
D)0.75
E)0.77

Quizplus · Accepted Answer

To find the standard deviation, first calculate the mean (expected value) of the number of storms: $E(X) = 0(0.1) + 1(0.2) + 2(0.4) + 3(0.3) = 1.7$. Then, calculate the variance: $Var(X) = (0-1.7)^2(0.1) + (1-1.7)^2(0.2) + (2-1.7)^2(0.4) + (3-1.7)^2(0.3) = 0.81$. The standard deviation is the square root of the variance: $\sqrt{0.81} = 0.9$. The closest answer is 0.94.