Let's fill in the missing information step by step.
First, let's find the boundary height for the segment from 0 to +1 standard deviation:
- The mean height is 60 inches.
- The standard deviation is 12 inches.
- From 0 to +1 standard deviation is from 60 inches to (mean + 1 standard deviation) = 60 + 12 = 72 inches.
Next, let's determine the percentage from 0 to +1 standard deviation:
- Given that there are 500 trees in total and 171 of them fall into the 0 to +1 standard deviation segment.
- The percentage of trees in this segment is (171 / 500) 100 = 34.2%.
Finally, let's determine the number of trees from +1 to +2 standard deviation:
- The standard deviation from +1 to +2 corresponds to 13.6% of the distribution.
- The number of trees in this segment is (13.6 / 100) 500 = 68 trees.
Therefore, the completed table is:
\begin{tabular}{|c|c|c|}
\hline Standard Deviation & Percentage from table & Number of trees out of 500 \\
\hline -1 to 0 (48 to 60 inches) & 34.1\% & 171 \\
\hline 0 to +1 (60 to 72 inches) & 34.2\% & 171 \\
\hline +1 to +2 (72 to 84 inches) & 13.6\% & 68 \\
\hline
\end{tabular}
