emancipezN

2020-12-12

Census data are often used to obtain probability distributions for various random variables. Census data for families in a particular state with a combined income of \$50,000 or more show that 22% of these families have no children, 30% have one child, 27% have two children, and 21% have three children. From this information, construct the probability distribution for x, where x represents the number of children per family for this income group. (Give your answers correct to two decimal places.) $P\left(0\text{children}\right)=$
$P\left(1\text{child}\right)=$
$P\left(2\text{children}\right)=$
$P\left(3\text{children}\right)=$

Mayme

Step 1 Here, the given data is:

No Children $=22\mathrm{%}$

One Child $=30\mathrm{%}$

Two Chidren $=27\mathrm{%}$

Three Children $=21\mathrm{%}$

Total $\mathrm{%}=22\mathrm{%}+30\mathrm{%}+27\mathrm{%}+21\mathrm{%}$

Total $\mathrm{%}=100\mathrm{%}$

Step 2

The probability distribution table is:

$\begin{array}{cc}X& P\left(X\right)\\ 0& 22/100=0.22\\ 1& 30/100=0.30\\ 2& 27/100=0.27\\ 3& 21/100=0.21\end{array}$

$P\left(0\right)=0.22$

$P\left(1\right)=0.30$

$P\left(2\right)=0.27$

$P\left(3\right)=0.21$

Do you have a similar question?