Of course, let's go through each part of the question step by step.
### Part (a) Construct a relative frequency distribution of the data.
First, we need to organize the given data into a relative frequency distribution table. Here's the table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Response} & \text{Relative Frequency} \\
\hline
\text{Never} & 0.138 \\
\text{Rarely} & 0.194 \\
\text{Sometimes} & 0.420 \\
\text{Most of the time} & 0.212 \\
\text{Always} & 0.036 \\
\hline
\end{array}
\][/tex]
The relative frequencies for each response category are already provided, and they are rounded to three decimal places. This table represents how frequently each response occurs relative to the total number of responses.
### Part (b) What percentage of respondents answered "Always"?
To find the percentage of respondents who answered "Always," we take the relative frequency of the "Always" response and convert it to a percentage.
The relative frequency for "Always" is [tex]\(0.036\)[/tex].
To convert this to a percentage, we multiply by 100:
[tex]\[ 0.036 \times 100 = 3.6 \][/tex]
Thus, the percentage of respondents who answered "Always" is [tex]\(3.6\%\)[/tex].
[tex]\[
\boxed{3.6\%}
\][/tex]
To summarize:
- The relative frequency distribution table is organized with the given relative frequencies.
- The percentage of respondents who answered "Always" is [tex]\(3.6\%\)[/tex], rounded to one decimal place.
