Solve the problem.
-In a certain town, 40% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults)who have a college degree. Find the standard deviation for the probability distribution. $$\begin{array} { c | c }
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.1296 \
\hline 1 & 0.3456 \
\hline 2 & 0.3456 \
\hline 3 & 0.1536 \
\hline 4 & 0.0256
\end{array}$$
A)0.96
B)1.12
C)1.88
D)0.98

Question

Solve the problem.
-In a certain town, 40% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults)who have a college degree. Find the standard deviation for the probability distribution. $$\begin{array} { c | c } 
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.1296 \
\hline 1 & 0.3456 \
\hline 2 & 0.3456 \
\hline 3 & 0.1536 \
\hline 4 & 0.0256
\end{array}$$
A)0.96
B)1.12
C)1.88
D)0.98

Quizplus · Accepted Answer

The standard deviation of a probability distribution is calculated using the formula $\sigma = \sqrt{\sum (x - \mu)^2 \cdot P(x)}$, where $\mu$ is the mean of the distribution. First, calculate the mean: $\mu = 0(0.1296) + 1(0.3456) + 2(0.3456) + 3(0.1536) + 4(0.0256) = 1.6$. Then, calculate the standard deviation: $\sigma = \sqrt{(0-1.6)^2(0.1296) + (1-1.6)^2(0.3456) + (2-1.6)^2(0.3456) + (3-1.6)^2(0.1536) + (4-1.6)^2(0.0256)} \approx 0.98$.

Solve the Problem A)096 B)1

Solve the Problem A)096
B)1