To find the largest plausible value for the mean height of the plants in the nursery, we start with the mean height, which is 49 inches.
Next, we calculate the margin of error in absolute terms. The margin of error is given as a percentage, specifically 3.8% of the mean height.
First, we calculate 3.8% of 49 inches:
\[ \text{Margin of Error} = 0.038 \times 49 \]
Calculating this:
\[ 0.038 \times 49 = 1.862 \]
Now, we find the largest plausible value for the mean height by adding the margin of error to the mean height:
\[ \text{Largest plausible value} = \text{Mean height} + \text{Margin of Error} \]
\[ \text{Largest plausible value} = 49 + 1.862 = 50.862 \]
Rounding to the nearest tenth of an inch:
\[ \text{Largest plausible value} \approx 50.9 \text{ inches} \]
Thus, the largest plausible value for the mean height of the plants in this nursery is 50.9 inches.