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?

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 Dogs01 class=


Answer :

[tex]\sum ^n_{i\mathop=1}\frac{\text{xiP(x)}}{N}=\frac{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}=\frac{0.61}{1}=0.6[/tex]

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

[tex]\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}[/tex][tex]s=\sqrt[]{\frac{0.9179}{1}}=0.958\approx0.96[/tex]