Question

complete parts (a) and (b) below. the number of dogs per household in a small town dogs 0 1 2 3 4 5 probability 0.687 0.196 0.075 0.021 0.013 0.008 (a) find the mean, variance, and standard deviation of the probability distribution. find the mean of the probability distribution. μ = (round to one decimal place as needed.)

Explanation:

Step1: Recall mean formula

The formula for the mean $\mu$ of a discrete - probability distribution is $\mu=\sum_{x}x\cdot P(x)$, where $x$ is the value of the random variable and $P(x)$ is the corresponding probability.
\[

$$\begin{align*} \mu&=(0\times0.687)+(1\times0.196)+(2\times0.075)+(3\times0.021)+(4\times0.013)+(5\times0.008)\\ \end{align*}$$

\]

Step2: Calculate each product

\[

$$\begin{align*} 0\times0.687& = 0\\ 1\times0.196&=0.196\\ 2\times0.075& = 0.15\\ 3\times0.021&=0.063\\ 4\times0.013&=0.052\\ 5\times0.008&=0.04 \end{align*}$$

\]

Step3: Sum up the products

\[

$$\begin{align*} \mu&=0 + 0.196+0.15+0.063+0.052+0.04\\ &=0.491\approx0.5 \end{align*}$$

\]

Answer:

$0.5$