complete parts (a) and (b) below.
the number of dogs per household in a small town
dogs
0
1
2
3
4
5
probability
0.690
0.190
0.079
0.022
0.013
0.006
(a) find the mean, variance, and standard deviation of the probability distribution.
find the mean of the probability distribution.
μ = 0.5 (round to one decimal place as needed.)
find the variance of the probability distribution.
σ² = 0.8 (round to one decimal place as needed.)

Question

Accepted Answer

# Explanation:
## Step1: Calculate the mean ($\mu$)
The formula for the mean of a discrete probability distribution is $\mu=\sum(x\times P(x))$.
$$
\begin{align*}
\mu&=(0\times0.690)+(1\times0.190)+(2\times0.079)+(3\times0.022)+(4\times0.013)+(5\times0.006)\
&=0 + 0.190+0.158 + 0.066+0.052+0.030\
&=0.5
\end{align*}
$$
## Step2: Calculate the variance ($\sigma^{2}$)
The formula for the variance is $\sigma^{2}=\sum((x - \mu)^{2}\times P(x))$.
$$
\begin{align*}
\sigma^{2}&=((0 - 0.5)^{2}\times0.690)+((1 - 0.5)^{2}\times0.190)+((2 - 0.5)^{2}\times0.079)+((3 - 0.5)^{2}\times0.022)+((4 - 0.5)^{2}\times0.013)+((5 - 0.5)^{2}\times0.006)\
&=(0.25\times0.690)+(0.25\times0.190)+(2.25\times0.079)+(6.25\times0.022)+(12.25\times0.013)+(20.25\times0.006)\
&=0.1725+0.0475 + 0.17775+0.1375+0.15925+0.1215\
&=0.8
\end{align*}
$$
## Step3: Calculate the standard deviation ($\sigma$)
The formula for the standard deviation is $\sigma=\sqrt{\sigma^{2}}$. Since $\sigma^{2} = 0.8$, then $\sigma=\sqrt{0.8}\approx0.9$

# Answer:
Mean ($\mu$) = $0.5$, Variance ($\sigma^{2}$) = $0.8$, Standard deviation ($\sigma$) $\approx0.9$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the mean ($\mu$)

Step2: Calculate the variance ($\sigma^{2}$)

Step3: Calculate the standard deviation ($\sigma$)

Answer: