Provide an appropriate response. Round to the nearest hundredth.
-The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate Office. Its probability distribution is as follows. Find the standard deviation for the probability distribution.

$\begin{array}{c|c}
\text { Houses Sold }(\mathrm{x}) & \text { Probability } \mathrm{P}(\mathrm{x}) \
\hline 0 & 0.24 \
1 & 0.01 \
2 & 0.12 \
3 & 0.16 \
4 & 0.01 \
5 & 0.14 \
6 & 0.11 \
7 & 0.21
\end{array}$
A) $\sigma = 2.25$
B) $\sigma = 4.45$
C) $\sigma = 6.86$
D) $\sigma = 2.62$

Question

Provide an appropriate response. Round to the nearest hundredth.
-The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate Office. Its probability distribution is as follows. Find the standard deviation for the probability distribution.

$\begin{array}{c|c}
\text { Houses Sold }(\mathrm{x}) & \text { Probability } \mathrm{P}(\mathrm{x}) \
\hline 0 & 0.24 \
1 & 0.01 \
2 & 0.12 \
3 & 0.16 \
4 & 0.01 \
5 & 0.14 \
6 & 0.11 \
7 & 0.21
\end{array}$
A) $\sigma = 2.25$
B) $\sigma = 4.45$
C) $\sigma = 6.86$
D) $\sigma = 2.62$

Quizplus · Accepted Answer

The standard deviation is the square root of the variance. The variance is calculated as the sum of the squared deviations from the mean, weighted by their probabilities. The mean is calculated as the sum of the products of the values and their probabilities.$\mu = \sum xP(x) = 0(0.24) + 1(0.01) + 2(0.12) + 3(0.16) + 4(0.01) + 5(0.14) + 6(0.11) + 7(0.21) = 3.67$$\sigma^2 = \sum (x - \mu)^2P(x) = (0 - 3.67)^2(0.24) + (1 - 3.67)^2(0.01) + (2 - 3.67)^2(0.12) + (3 - 3.67)^2(0.16) + (4 - 3.67)^2(0.01) + (5 - 3.67)^2(0.14) + (6 - 3.67)^2(0.11) + (7 - 3.67)^2(0.21) = 6.86$$\sigma = \sqrt{6.86} = 2.62$

Provide an Appropriate Response A) σ=2.25\sigma = 2.25σ=2.25 B) σ=4.45\sigma = 4.45σ=4.45

Provide an Appropriate Response A) $\sigma = 2.25$ B) $\sigma = 4.45$