To create the relative frequency table, you need to express each number in the original table as a percentage of the total number of customers surveyed. Here’s a step-by-step solution to fill in the relative frequency table:
1. Determine the relative frequencies for each category by dividing the frequency by the total number surveyed (200) and then multiplying by 100 to get the percentage.
2. Relative Frequency for Satisfied Customers with Plan A:
- There are 104 satisfied customers out of 200 total customers.
- [tex]\( \frac{104}{200} \times 100 = 52\% \)[/tex]
3. Relative Frequency for Satisfied Customers with Plan B:
- There are 64 satisfied customers out of 200 total customers.
- [tex]\( \frac{64}{200} \times 100 = 32\% \)[/tex]
4. Relative Frequency for Total Satisfied Customers:
- There are 168 satisfied customers out of 200 total customers.
- [tex]\( \frac{168}{200} \times 100 = 84\% \)[/tex]
5. Relative Frequency for Not Satisfied Customers with Plan A:
- There are 8 not satisfied customers out of 200 total customers.
- [tex]\( \frac{8}{200} \times 100 = 4\% \)[/tex]
6. Relative Frequency for Not Satisfied Customers with Plan B:
- There are 24 not satisfied customers out of 200 total customers.
- [tex]\( \frac{24}{200} \times 100 = 12\% \)[/tex]
7. Relative Frequency for Total Not Satisfied Customers:
- There are 32 not satisfied customers out of 200 total customers.
- [tex]\( \frac{32}{200} \times 100 = 16\% \)[/tex]
8. Relative Frequency for Total Customers having Plan A:
- There are 112 customers with Plan A out of 200 total customers.
- [tex]\( \frac{112}{200} \times 100 = 56\% \)[/tex]
9. Relative Frequency for Total Customers having Plan B:
- There are 88 customers with Plan B out of 200 total customers.
- [tex]\( \frac{88}{200} \times 100 = 44\% \)[/tex]
Now, place the calculated percentages into the relative frequency table:
\begin{tabular}{|c|c|c|c|}
\hline & Plan A & Plan B & Total \\
\hline Satisfied & 52\% & 32\% & 84\% \\
\hline Not satisfied & 4\% & 12\% & 16\% \\
\hline Total & 56\% & 44\% & 100\% \\
\hline
\end{tabular}
So, the table with the correct answers filled is:
\begin{tabular}{|c|c|c|c|}
\hline & Plan A & Plan B & Total \\
\hline Satisfied & 52\% & 32\% & 84\% \\
\hline Not satisfied & 4\% & 12\% & 16\% \\
\hline Total & 56\% & 44\% & 100\% \\
\hline
\end{tabular}
