Chapter 4, Problem 88RE

(a)

To determine

To draw: a scatter diagram of the given data.

Answer to Problem 88RE

From the scatter plot, the relation that exists between two variables appears tobe cubic.

  

Explanation of Solution

Given:

  

Calculation:

The scatter diagram as follow:

  

From the scatter plot we can see that the relation that exists between two variables appears tobe cubic.

Conclusion:

Thus, the scatter diagram is drawn.

(b)

To determine

To predict: the percentage of U.S. families that were below the poverty level

Answer to Problem 88RE

The percentage of U.S. families that were below poverty line is 11.472%.

Explanation of Solution

Calculation:

From the graph, cubic function is the best fit to these data because cubic

Curve is passing from most of the points and it is capturing the change in the data better than the other functions.

  

The cubic function is,

  $f(x)=0.0095x^3-0.22x^2+1.18x+10$

In 2005, the percentage of U.S. families that were below poverty line can be calculated bysubstituting $x=16$ in cubic function,

  $f(16)=0.0095{(16)}^3-0.22{(16)}^2+1.18(16)+10=38.912-56.32+18.88+10=11.472$

Conclusion:

The percentage of U.S. families that were below poverty line is 11.472%

(c)

To determine

To draw: the function of best fit on the scatter diagram drawn in part (a).

Answer to Problem 88RE

  

Explanation of Solution

Calculation:

The graph of cubic function is as follows,

  

Conclusion:

Thus, the required graph is drawn.