The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. $$\begin{array} { | c | c | }
\hline \mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 1 & 0.14 \
2 & 0.16 \
3 & 0.12 \
4 & 0.14 \
5 & 0.13 \
6 & 0.31 \
\hline
\end{array}$$
A) $\mu = 3.89$
B) $\mu = 3.76$
C) $\mu = 0.17$
D) $\mu = 3.50$

Question

The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. $$\begin{array} { | c | c | } 
\hline \mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 1 & 0.14 \
2 & 0.16 \
3 & 0.12 \
4 & 0.14 \
5 & 0.13 \
6 & 0.31 \
\hline
\end{array}$$ 
A) $\mu = 3.89$
B) $\mu = 3.76$
C) $\mu = 0.17$
D) $\mu = 3.50$

Quizplus · Accepted Answer

The mean of a probability distribution is the expected value, which is calculated by multiplying each possible outcome by its probability and then summing the results. In this case, the mean is:$\mu = 1(0.14) + 2(0.16) + 3(0.12) + 4(0.14) + 5(0.13) + 6(0.31) = 3.89$

The Accompanying Table Shows the Probability Distribution for X, the Number