Question

The number of dogs per household in a neighborhood is given in the probabilitydistribution. Find the mean and the standard deviation. Round to 1 decimal.# of Dogs0123stP(x)0.620.240.070.05.02a) What is the mean rounded to 2 decimal place?b) What is the standard deviation rounded to 2 decimal place?

Answer 1

`\sum ^n_(i\mathop=1)\frac{\text{xiP(x)}}{N}=(0\cdot0.62+1\cdot0.24+2\cdot0.07+3\cdot0.05+4\cdot0.02)/(0.62+0.24+0.07+0.05+0.02)=(0.61)/(1)=0.6`

`s=\sqrt[]{((x-\mu)^2p(x))/(n)}`

`\begin{gathered} \sum ^n_(i\mathop=1)(x-\mu)^2p(x)=(0-0.61)^20.62+(1-0.61)^20.24+(2-0.61)^20.07+.. \\ \text{ (3-0.61)}^20.05+(4-0.61)^20.02=0.9179 \\ \end{gathered}`
`s=\sqrt[]{(0.9179)/(1)}=0.958\approx0.96`