To find the difference between the mean heights of the two samples, we first need to calculate the mean height for each sample.
Sample 1 Heights: 85.4, 87.6, 87.1, 85.6, 85.9, 85.3, 84.9, 83.7, 84.0, 85.2
Calculating the Mean for Sample 1:
\[ \text{Mean} = \frac{\text{Sum of heights}}{\text{Number of trees}} \]
Calculating the sum of the heights for Sample 1:
\[ 85.4 + 87.6 + 87.1 + 85.6 + 85.9 + 85.3 + 84.9 + 83.7 + 84.0 + 85.2 = 860.7 \]
Now, calculate the mean:
\[ \text{Mean}_1 = \frac{860.7}{10} = 86.07 \]
Sample 2 Heights: 87.1, 88.0, 84.2, 85.3, 86.5, 84.2, 83.2, 84.1, 85.2, 87.3
Calculating the Mean for Sample 2:
Calculating the sum of the heights for Sample 2:
\[ 87.1 + 88.0 + 84.2 + 85.3 + 86.5 + 84.2 + 83.2 + 84.1 + 85.2 + 87.3 = 860.1 \]
Now, calculate the mean:
\[ \text{Mean}_2 = \frac{860.1}{10} = 86.01 \]
Calculating the Difference Between the Means:
\[ \text{Difference} = \text{Mean}_1 - \text{Mean}_2 = 86.07 - 86.01 = 0.06 \]
Therefore, the difference between the mean heights of the trees of these two random samples is \( \boxed{0.06} \).