Chapter 1, Problem R1.8RE

(a)

To determine

To compute: The percent of each group of households consisted of four or more people.

Answer to Problem R1.8RE

The percent of lower and higher income group of households consisted of four or more people, is approximately 10 and 41 percent, respectively.

Explanation of Solution

Given:

As per the given graph of low-income household, the approximately distribution can be written as:

X	1	2	3	4	5	6	7
P(x)	0.60	0.20	0.10	0.05	0.025	0.013	0.012

As per the given graph of high-income household, the approximately distribution can be written as:

X	1	2	3	4	5	6	7
P(x)	0.05	0.34	0.20	0.23	0.12	0.04	0.02

Calculation:

For the lower income group,

The percent of each group of households consisted of four or more people, can be calculated as:

  $\begin{array}{c}P\left(X\ge 4\right)=P\left(X=4\right)+P\left(X=5\right)+P\left(X=6\right)+P\left(X=7\right)\\ =0.05+0.025+0.013+0.012\\ =0.10\end{array}$

For the higher income group,

The percent of each group of households consisted of four or more people, can be calculated as:

  $\begin{array}{c}P\left(X\ge 4\right)=P\left(X=4\right)+P\left(X=5\right)+P\left(X=6\right)+P\left(X=7\right)\\ =0.23+0.12+0.04+0.02\\ =0.41\end{array}$

(b)

To determine

To explain:The similarities and differences in these two distributions of household size.

Explanation of Solution

Given: As per the above sub − part a,

Similarities,

Both graphs display the continuous data set and present the data set using histogram plot.

The number of bins and the class interval are the same in both histogram plots.

Difference,

The above plot of histogram represents the lower income while the below plot of histogram represents the higher income of households.

The lower income plot, is a right skewed while the higher income plot, is approximately normal.