To complete the given relative frequency table, let's analyze the provided data step-by-step:
1. Understand the Given Data:
First, let's look at the completed part of the relative frequency table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & U & V & Total \\
\hline S & 26\% & 42\% & 68\% \\
\hline T & 21\% & k & 32\% \\
\hline Total & 47\% & 53\% & 100\% \\
\hline
\end{tabular}
\][/tex]
- The total percentages in each row and column must add up to 100%.
- The missing value [tex]\( k \)[/tex] in the column V for the row T needs to be determined.
2. Find the Percentage for U in Row T:
From the given data:
- The total percentage for the T row is 32%.
- For T with U, it is stated to be 68%, which includes both S and T.
Therefore, we need to segregate S and T in U:
- For S, U is 26%.
- The total for T from 100% value for U should leave us 32%.
3. Calculate the Percentage for T in U:
[tex]\[
\text{Total percentage for T (in U and V)} = 32\%
\][/tex]
Adding the percentage of T in U:
[tex]\[
32\% - 26\% = 68\%
\][/tex]
4. Update the Relative Frequency Table:
By fitting these values into the relative frequency table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & U & V & Total \\
\hline S & 26\% & 42\% & 68\% \\
\hline T & 68\% & k(complete) & 32\% \\
\hline Total & 100\% & 100\% & 100\% \\
\hline
\end{tabular}
\][/tex]
Therefore
\[
\begin{tabular}{|c|c|c|c|}
\hline & U & V & Total \\
\hline S & 26\% & 42\% & 68\% \\
\hline T & 68\% kill & 32\% \\
\hline Total & 100\% & 100\% & 100\% \\
\hline
\end{tabular}
5. Verification:
Check if component T with V good,We find it fits with the provided value.
