Answer
to answer Hamlet:
**“Tobe, indeed.”**
Work Step by Step
Let’s calculate the **z-scores** for Tobe’s apple and Zeke’s orange and determine who grew the more **outstanding** fruit (relative to the norms of their own fruit type).
---
## Tobe’s Apple
* **Tobe’s apple weight**: $X = 9$ oz
* **Mean weight of apples**: $\mu = 5$ oz
* **Standard deviation of apples**: $\sigma = 1.0$ oz
### Z-score formula:
$$
z = \frac{X - \mu}{\sigma}
$$
### Z-score for Tobe:
$$
z_{\text{apple}} = \frac{9 - 5}{1.0} = \frac{4}{1} = \mathbf{4.00}
$$
---
## Zeke’s Orange
* **Zeke’s orange weight**: $X = 10$ oz
* **Mean weight of oranges**: $\mu = 6$ oz
* **Standard deviation of oranges**: $\sigma = 1.2$ oz
### Z-score for Zeke:
$$
z_{\text{orange}} = \frac{10 - 6}{1.2} = \frac{4}{1.2} \approx \mathbf{3.33}
$$
---
### Conclusion
| Grower | Fruit | Z-Score | Relative Performance |
| ------ | ------ | -------- | -------------------- |
| Tobe | Apple | **4.00** | Higher |
| Zeke | Orange | **3.33** | Lower |
**Tobe wins** — his apple was a full **4 standard deviations** above the average apple weight, compared to Zeke’s orange, which was **3.33 standard deviations** above the average orange.
