To solve this problem, we need to follow these steps:
1. Identify the shaded rows from the table.
2. Calculate the sample mean for each of the shaded rows.
3. Determine the range of these sample means.
First, let's identify the shaded rows:
- The 2nd row: [tex]\(4, 2, 3, 0, 5\)[/tex]
- The 3rd row: [tex]\(0, 1, 1, 2, 0\)[/tex]
- The 5th row: [tex]\(3, 2, 0, 1, 4\)[/tex]
Next, we calculate the sample mean for each of these rows.
For the 2nd row ([tex]\(4, 2, 3, 0, 5\)[/tex]):
[tex]\[
\text{Mean}_1 = \frac{4 + 2 + 3 + 0 + 5}{5} = \frac{14}{5} = 2.8
\][/tex]
For the 3rd row ([tex]\(0, 1, 1, 2, 0\)[/tex]):
[tex]\[
\text{Mean}_2 = \frac{0 + 1 + 1 + 2 + 0}{5} = \frac{4}{5} = 0.8
\][/tex]
For the 5th row ([tex]\(3, 2, 0, 1, 4\)[/tex]):
[tex]\[
\text{Mean}_3 = \frac{3 + 2 + 0 + 1 + 4}{5} = \frac{10}{5} = 2.0
\][/tex]
Now, we have the three sample means: [tex]\(2.8\)[/tex], [tex]\(0.8\)[/tex], and [tex]\(2.0\)[/tex].
To find the range of these sample means:
[tex]\[
\text{Range} = \text{Maximum mean} - \text{Minimum mean}
\][/tex]
The maximum mean is [tex]\(2.8\)[/tex] and the minimum mean is [tex]\(0.8\)[/tex]:
[tex]\[
\text{Range} = 2.8 - 0.8 = 2.0
\][/tex]
Thus, the range of the values for the sample means is:
[tex]\[
\boxed{2}
\][/tex]
