Find the standard deviation of the random variable.
-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 given in the table. Round the answer to two decimal
Places. $\begin{array}{c|cccccccc}
\text { Houses Sold (x) } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \text { Probability } \mathrm{P}(\mathrm{x}) & 0.24 & 0.01 & 0.12 & 0.16 & 0.01 & 0.14 & 0.11 & 0.21
\end{array}$
A)$6.86$
B) $4.45$
C) $2.62$
D) $2.25$

Question

Quizplus · Accepted Answer

To find the standard deviation of a discrete random variable, we first need to calculate its mean ($\mu$) and then use the formula for the standard deviation ($\sigma$) which involves summing the squared differences between each value and the mean, weighted by their probabilities. 1. Calculate the mean ($\mu$):$\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) = 3.59$2. Calculate the variance ($\sigma^2$):$\sigma^2 = \sum (x - \mu)^2P(x)$$\sigma^2 = (0-3.59)^2(0.24) + (1-3.59)^2(0.01) + (2-3.59)^2(0.12) + (3-3.59)^2(0.16) + (4-3.59)^2(0.01) + (5-3.59)^2(0.14) + (6-3.59)^2(0.11) + (7-3.59)^2(0.21)$$\sigma^2 = 6.8641$3. Calculate the standard deviation ($\sigma$):$\sigma = \sqrt{\sigma^2} = \sqrt{6.8641} \approx 2.62$Therefore, the standard deviation of the random variable is approximately 2.62.

Find the Standard Deviation of the Random Variable A) 6.866.866.86 B) 4.454.454.45

Find the Standard Deviation of the Random Variable A) $6.86$ B) $4.45$