https://file.aiquickdraw.com/mathbot/file/1726293554164oyzq98vx.jpg

Let's break down the problem in the image.

### Given:
- The mean foot length for adult males: \( \mu = 26.72 \) cm
- Standard deviation: \( \sigma = 1.28 \) cm

You are asked to use the **empirical rule** (which states that for a normal distribution):
- 68% of data falls within 1 standard deviation (\( \mu \pm 1\sigma \))
- 95% of data falls within 2 standard deviations (\( \mu \pm 2\sigma \))
- 99.7% of data falls within 3 standard deviations (\( \mu \pm 3\sigma \))

This rule helps define **significantly low** and **significantly high** values.

#### To find:
- **Significantly low values**: Less than \( \mu - 2\sigma \)
- **Significantly high values**: Greater than \( \mu + 2\sigma \)

Now, let's compute the values using the empirical rule.

1. **Lower boundary (significantly low)**:  
   \( \mu - 2\sigma = 26.72 - 2 \times 1.28 \)
   
2. **Upper boundary (significantly high)**:  
   \( \mu + 2\sigma = 26.72 + 2 \times 1.28 \)

I'll calculate these now.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through the calculations manually. Here's how:

1. **Lower boundary (significantly low)**:  
   \( \mu - 2\sigma = 26.72 - 2 \times 1.28 = 26.72 - 2.56 = 24.16 \) cm.

2. **Upper boundary (significantly high)**:  
   \( \mu + 2\sigma = 26.72 + 2 \times 1.28 = 26.72 + 2.56 = 29.28 \) cm.

So:
- **Significantly low values** are **24.16 cm or lower**.
- **Significantly high values** are **29.28 cm or higher**.

Now, let's evaluate the foot length of **29.6 cm**:
- Since 29.6 cm is **greater than 29.28 cm**, it falls into the category of **significantly high**.

Would you like more clarification on any step, or help with the next part of the problem?

Here are some follow-up questions you might consider:
1. How does the empirical rule apply to a normal distribution?
2. What is the range of values that are not considered significant?
3. What happens when we extend to 3 standard deviations?
4. Could we calculate the z-score for the 29.6 cm foot length?
5. How does this method change with non-normal distributions?

**Tip:** Using z-scores is another great way to check how far a value is from the mean.

A group of adult males has foot lengths with a mean of 26.72 cm and a standard deviation of 1.28 cm. Use the range rule of thumb for identifying significant values to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 29.6 cm significantly low or significantly high? Explain.

Analyze whether a male foot length of 29.6 cm is significantly high using the empirical rule, given a mean of 26.72 cm and a standard deviation of 1.28 cm. Learn about standard deviation limits and how to apply the 68-95-99.7 rule to a normal distribution.

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