Answered

A survey of 150 students was taken. It was determined that [tex]$\frac{2}{3}$[/tex] of the students play video games. Of the students that play video games, 85 also use social media. Of the students that do not play video games, [tex]$20\%$[/tex] do not use social media.

Complete the two-way frequency table.
\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & \begin{tabular}{c}
Play Video \\
Games
\end{tabular} & \begin{tabular}{c}
Do Not Play \\
Video Games
\end{tabular} & Total \\
\hline Social Media & & & \\
\hline \begin{tabular}{c}
No Social \\
Media
\end{tabular} & & & \\
\hline Total & & & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To complete the two-way frequency table, we can proceed step by step to fill in each of the cells in the table.

1. Total number of students:
[tex]\[ \text{Total} = 150 \][/tex]

2. Number of students who play video games:
[tex]\[ \text{Play Video Games} = \left(\frac{2}{3}\right) \times 150 = 100 \][/tex]

3. Number of students who do not play video games:
[tex]\[ \text{Do Not Play Video Games} = 150 - 100 = 50 \][/tex]

4. Of the students who play video games, the number who also use social media:
[tex]\[ \text{Play Video Games and Use Social Media} = 85 \][/tex]

5. Number of students who play video games and do not use social media:
[tex]\[ \text{Play Video Games and Do Not Use Social Media} = 100 - 85 = 15 \][/tex]

6. Of the students who do not play video games, 20% do not use social media:
[tex]\[ \text{Do Not Play Video Games and Do Not Use Social Media} = 0.20 \times 50 = 10 \][/tex]

7. Number of students who do not play video games and use social media:
[tex]\[ \text{Do Not Play Video Games and Use Social Media} = 50 - 10 = 40 \][/tex]

8. Total number of students who use social media:
[tex]\[ \text{Total Use Social Media} = 85 + 40 = 125 \][/tex]

9. Total number of students who do not use social media:
[tex]\[ \text{Total Do Not Use Social Media} = 15 + 10 = 25 \][/tex]

Now, constructing the two-way frequency table with all the calculated values:

[tex]\[ \begin{array}{|c|c|c|c|} \cline{2-4} \multicolumn{1}{c|}{} & \text{Play Video} & \text{Do Not Play} & \text{Total} \\ \multicolumn{1}{c|}{} & \text{Games} & \text{Video Games} & \\ \hline \text{Social Media} & 85 & 40 & 125 \\ \hline \text{No Social Media} & 15 & 10 & 25 \\ \hline \text{Total} & 100 & 50 & 150 \\ \hline \end{array} \][/tex]

So, the completed two-way frequency table is:

[tex]\[ \begin{array}{|c|c|c|c|} \cline{2-4} \multicolumn{1}{c|}{} & \text{Play Video} & \text{Do Not Play} & \text{Total} \\ \multicolumn{1}{c|}{} & \text{Games} & \text{Video Games} & \\ \hline \text{Social Media} & 85 & 40 & 125 \\ \hline \text{No Social Media} & 15 & 10 & 25 \\ \hline \text{Total} & 100 & 50 & 150 \\ \hline \end{array} \][/tex]