To find the percentage area associated with given units of standard deviation using the provided table, we'll look up the area corresponding to each specified standard deviation value. The standard deviation values we are interested in are 2.6, 1.4, 0.2, 1.8, and 3.8. Here are the detailed steps and results:
1. Standard Deviation 2.6:
- From the table, the area associated with [tex]\( x = 2.6 \)[/tex] is 0.4953.
2. Standard Deviation 1.4:
- From the table, the area associated with [tex]\( x = 1.4 \)[/tex] is 0.4192.
3. Standard Deviation 0.2:
- From the table, the area associated with [tex]\( x = 0.2 \)[/tex] is 0.0793.
4. Standard Deviation 1.8:
- From the table, there are two entries for [tex]\( x = 1.8 \)[/tex], but we will use the first one we encounter, which is 0.4641.
5. Standard Deviation 3.8:
- From the table, there are two entries for [tex]\( x = 3.8 \)[/tex], but we will use the first one we encounter, which is 0.4999.
After identifying each area from the table, the percentage for each standard deviation value is as follows:
- For [tex]\( x = 2.6 \)[/tex], the percentage is [tex]\( 0.4953 \times 100\% = 49.53\% \)[/tex].
- For [tex]\( x = 1.4 \)[/tex], the percentage is [tex]\( 0.4192 \times 100\% = 41.92\% \)[/tex].
- For [tex]\( x = 0.2 \)[/tex], the percentage is [tex]\( 0.0793 \times 100\% = 7.93\% \)[/tex].
- For [tex]\( x = 1.8 \)[/tex], the percentage is [tex]\( 0.4641 \times 100\% = 46.41\% \)[/tex].
- For [tex]\( x = 3.8 \)[/tex], the percentage is [tex]\( 0.4999 \times 100\% = 49.99\% \)[/tex].
So, the completed table will be:
\begin{tabular}{|l|l|}
\hline Standard Deviation & Percentage Area \\
\hline 2.6 & 49.53\% \\
\hline 1.4 & 41.92\% \\
\hline 0.2 & 7.93\% \\
\hline 1.8 & 46.41\% \\
\hline 3.8 & 49.99\% \\
\hline & \\
\hline
\end{tabular}
