Question 1191372
Here's how to determine the minimum size limit:

1. **Find the z-score:** We want to find the length below which 18% (100% - 82%) of the trout fall. We use a z-table or calculator to find the z-score corresponding to a cumulative probability of 0.82. A z-score of approximately 0.92 corresponds to 82% of the data.

2. **Use the z-score formula:**
   x = μ + zσ

   Where:
   * x is the minimum size limit we want to find.
   * μ is the mean length (13.4 inches).
   * σ is the standard deviation (1.4 inches).
   * z is the z-score (0.92).

3. **Calculate:**
   x = 13.4 + (0.92 * 1.4)
   x = 13.4 + 1.288
   x ≈ 14.69 inches

Therefore, the Department of Natural Resources should set a minimum size limit of approximately 14.69 inches.