The random variable x represents the number of computers that families have along with the correspondingprobabilities. Find the mean and standard deviation for the random variable x. $$\begin{array} { c | c }
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.49 \
1 & 0.05 \
2 & 0.32 \
3 & 0.07 \
4 & 0.07
\end{array}$$
A) mean: 1.18; standard deviation: 1.30
B) mean: 1.39; standard deviation: 0.64
C) mean: 1.39; standard deviation: 0.80
D) mean: 1.18; standard deviation: 0.64

Question

The random variable x represents the number of computers that families have along with the correspondingprobabilities. Find the mean and standard deviation for the random variable x. $$\begin{array} { c | c } 
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.49 \
1 & 0.05 \
2 & 0.32 \
3 & 0.07 \
4 & 0.07
\end{array}$$
A) mean: 1.18; standard deviation: 1.30
B) mean: 1.39; standard deviation: 0.64
C) mean: 1.39; standard deviation: 0.80
D) mean: 1.18; standard deviation: 0.64

Quizplus · Accepted Answer

To find the mean ($\mu$), multiply each value of $x$ by its probability and sum these products: $\mu = (0)(0.49) + (1)(0.05) + (2)(0.32) + (3)(0.07) + (4)(0.07) = 1.18$. For the standard deviation ($\sigma$), calculate the variance ($\sigma^2$) first by using $\sigma^2 = \sum [x^2P(x)] - \mu^2$, then take the square root of the variance to find $\sigma$. The calculations give a standard deviation of approximately 1.30.

The Random Variable X Represents the Number of Computers That