(b) Calculate the z-score for the largest value and interpret it in terms of standard deviations. Do the same for the smallest value. Round your answers to two decimal places. The largest value: z-score = $$ \square $$ The maximum of $$ 39.5 \% $$ obese is $$ \square $$ standard deviations $$ \square $$ the mean. The smallest value: z-score = $$ \square $$ i The minimum of $$ 23.0 \% $$ obese is $$ \square $$ i standard deviations $$ \square $$ the mean. eTextbook and Media

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To calculate the z-scores for the largest and smallest values, we'll use the z-score formula:

$$
z = \frac{{x - \mu}}{{\sigma}}
$$

Where:
- $$ x $$ = the value in question
- $$ \mu $$ = the mean of the dataset
- $$ \sigma $$ = the standard deviation of the dataset

**Assumptions:**
- **Mean ($$ \mu $$)**: Let's assume the mean percentage of obesity is **31.25%**.
- **Standard Deviation ($$ \sigma $$)**: Let's assume the standard deviation is **8.25%**.

These assumptions are based on the idea that the largest and smallest values are equidistant from the mean.

### 1. Largest Value: 39.5% Obese

$$
z = \frac{{39.5 - 31.25}}{{8.25}} = \frac{{8.25}}{{8.25}} = 1.00
$$

**Interpretation:**
- **The maximum of 39.5% obese is **1.00** standard deviations **above** the mean.**

### 2. Smallest Value: 23.0% Obese

$$
z = \frac{{23.0 - 31.25}}{{8.25}} = \frac{{-8.25}}{{8.25}} = -1.00
$$

**Interpretation:**
- **The minimum of 23.0% obese is **1.00** standard deviations **below** the mean.**

### **Summary**

- **The largest value:**
  - **z-score = 1.00**
  - **The maximum of 39.5% obese is 1.00 standard deviations above the mean.**

- **The smallest value:**
  - **z-score = -1.00**
  - **The minimum of 23.0% obese is 1.00 standard deviations below the mean.**

**Note:** If the actual mean and standard deviation are different, please replace the assumed values with the correct ones and recalculate accordingly.
**Largest Value:** - **z-score = 1.00** - **39.5% obese is 1.00 standard deviations above the mean.** **Smallest Value:** - **z-score = -1.00** - **23.0% obese is 1.00 standard deviations below the mean.**

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