Chapter 4.6, Problem 2BCYP

To determine

The percentage of Americans that play online games for the age of 18 years using linear interpolation for the data shown below.

Percent of Americans who Play Online Games
Age	15	20	30	40	50
Percent	81	54	37	29	25

Answer to Problem 2BCYP

The percentage of American is 64.13 for 18 years.

Explanation of Solution

Given information: The data for the percentage of Americans who play online games is shown as,

Percent of Americans who Play Online Games
Age	15	20	30	40	50
Percent	81	54	37	29	25

Calculation: From the given data the equation for line of fit or regression line using the calculator is written as,

  $y=-1.45x+\mathrm{90.23......}\left(1\right)$

Here $\left(x\right)$ represents the age of Americans whereas $\left(y\right)$ represents the percentage of Americans who play online games.

Now the age $\left(x=18\right)$ lies in the given data set, therefore using linear interpolation and plugging for $\left(x=18\right)$ in (1) gives the value of $\left(y\right)$ which will represent the percentage of Americans who play online games for the age 18 years.

Therefore from (1),

  $\begin{array}{c}y=-1.45\left(18\right)+\mathrm{90.23......}\left(\text{For }x=18\right)\\ =64.13\end{array}$

Hence, the percentage of Americans for 18 years age is estimated 64.13.