To determine which distribution has the greatest spread, we need to compare the standard deviations of the four distributions. The standard deviation is a measure of how spread out the values in a distribution are. The greater the standard deviation, the greater the spread of the distribution.
Here is the given data in the table format:
[tex]\[
\begin{array}{|l|r|r|}
\hline
& \text{Mean} & \text{Standard Deviation} \\
\hline
\text{Distribution 1} & 22 & 0.2 \\
\hline
\text{Distribution 2} & 21 & 0.8 \\
\hline
\text{Distribution 3} & 19 & 1.2 \\
\hline
\text{Distribution 4} & 20 & 3.2 \\
\hline
\end{array}
\][/tex]
To find which distribution has the greatest spread, we look at the standard deviations:
- Distribution 1: Standard Deviation = 0.2
- Distribution 2: Standard Deviation = 0.8
- Distribution 3: Standard Deviation = 1.2
- Distribution 4: Standard Deviation = 3.2
Comparing these values, we can see that the standard deviation of Distribution 4 is the highest, which is [tex]\(3.2\)[/tex].
Thus, Distribution 4 has the greatest spread.
[tex]\[
\boxed{\text{Distribution 4}}
\][/tex]
