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

Question

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

Quizplus · Accepted Answer

To find the standard deviation of the given probability distribution, we first calculate the mean ($\mu$) and then use it to calculate the variance ($\sigma^2$), from which the standard deviation ($\sigma$) is the square root.1. Calculate the mean ($\mu$):$\mu = \sum [x \cdot P(x)] = (0 \cdot 0.24) + (1 \cdot 0.01) + (2 \cdot 0.12) + (3 \cdot 0.16) + (4 \cdot 0.01) + (5 \cdot 0.14) + (6 \cdot 0.11) + (7 \cdot 0.21) = 3.59$2. Calculate the variance ($\sigma^2$):$\sigma^2 = \sum [(x - \mu)^2 \cdot P(x)]$= $(0 - 3.59)^2 \cdot 0.24 + (1 - 3.59)^2 \cdot 0.01 + (2 - 3.59)^2 \cdot 0.12 + (3 - 3.59)^2 \cdot 0.16 + (4 - 3.59)^2 \cdot 0.01 + (5 - 3.59)^2 \cdot 0.14 + (6 - 3.59)^2 \cdot 0.11 + (7 - 3.59)^2 \cdot 0.21$= $6.8641$3. Calculate the standard deviation ($\sigma$):$\sigma = \sqrt{\sigma^2} = \sqrt{6.8641} \approx 2.62$Therefore, the standard deviation of the probability distribution is approximately 2.62.

Solve the Problem A)686 B)4

Solve the Problem A)686
B)4