To compute the upper limit of the confidence interval for the mean weight of trout in the pond, we will use the following steps:
1. **Determine the sample mean and standard deviation**:
- Sample Mean (\( \bar{x} \)) = 560g
- Sample Standard Deviation (s) = 84g
- Sample size (n) = 36
2. **Choose the confidence level**:
We need to specify a confidence level. Common levels are 90%, 95%, and 99%. For this example, let's assume a 95% confidence level.
3. **Find the critical value (z-score)**:
For a 95% confidence level, the critical value (z) can be found using a z-table or calculator:
- The critical value for a 95% confidence level is approximately 1.96.
4. **Calculate the standard error (SE)**:
\[
SE = \frac{s}{\sqrt{n}} = \frac{84}{\sqrt{36}} = \frac{84}{6} = 14
\]
5. **Calculate the margin of error (ME)**:
\[
ME = z \times SE = 1.96 \times 14 = 27.44
\]
6. **Calculate the upper limit of the confidence interval**:
\[
\text{Upper limit} = \bar{x} + ME = 560 + 27.44 = 587.44
\]
Thus, the upper limit of the 95% confidence interval for the mean weight of trout is approximately **587.44 grams**.