The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. $\begin{array}{c|c}
\boldsymbol{x} & \boldsymbol{P}(\boldsymbol{x}) \
\hline 1 & 0.14 \
2 & 0.16 \
3 & 0.12 \
4 & 0.14 \
5 & 0.13 \
6 & 0.31
\end{array}$

A) $\mu = 3.9$
B) $\mu = 0.2$
C) $\mu = 3.5$
D) $\mu = 3.8$

Question

The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. $\begin{array}{c|c}
\boldsymbol{x} & \boldsymbol{P}(\boldsymbol{x}) \
\hline 1 & 0.14 \
2 & 0.16 \
3 & 0.12 \
4 & 0.14 \
5 & 0.13 \
6 & 0.31
\end{array}$

A) $\mu = 3.9$
B) $\mu = 0.2$
C) $\mu = 3.5$
D) $\mu = 3.8$

Quizplus · Accepted Answer

The mean ($\mu$) of a probability distribution is calculated by summing the products of each value of $x$ and its corresponding probability $P(x)$. For this distribution, $\mu = (1)(0.14) + (2)(0.16) + (3)(0.12) + (4)(0.14) + (5)(0.13) + (6)(0.31) = 3.9$.

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