A group of adult males has foot lengths with a mean of

26.6926.69

cm and a standard deviation of

1.251.25

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

23.823.8

cm significantly low or significantly​ high?
Significantly low values are

enter your response here

cm or lower.

​(Type an integer or a decimal. Do not​ round.)

Part 2

Significantly high values are

enter your response here

cm or higher.

​(Type an integer or a decimal. Do not​ round.)

Part 3

Select the correct choice below and fill in the answer​ box(es) to complete your choice.

A.

The adult male foot length of

23.823.8

cm is significantly

highhigh

because it is

greatergreater

than

enter your response here

cm.

​(Type an integer or a decimal. Do not​ round.)

B.

The adult male foot length of

23.823.8

cm is significantly

lowlow

because it is

lessless

than

enter your response here

cm.

​(Type an integer or a decimal. Do not​ round.)

C.

The adult male foot length of

23.823.8

cm is not significant because it is between

enter your response here

cm and

enter your response here

cm.

​(Type integers or decimals. Do not​ round.)

To solve this problem, we will use the "range rule of thumb," which states that significantly low values are at least 2 standard deviations below the mean, and significantly high values are at least 2 standard deviations above the mean.

### Part 1: Calculate the Limits for Significantly Low and High Values

**Mean (\(\mu\))**: 26.69 cm  
**Standard Deviation (\(\sigma\))**: 1.25 cm

#### Significantly Low Values:
To find the limit for significantly low values:
\[ \text{Significantly Low} = \mu - 2\sigma \]

\[ \text{Significantly Low} = 26.69 - 2(1.25) \]

\[ \text{Significantly Low} = 26.69 - 2.50 \]

\[ \text{Significantly Low} = 24.19 \, \text{cm} \]

#### Significantly High Values:
To find the limit for significantly high values:
\[ \text{Significantly High} = \mu + 2\sigma \]

\[ \text{Significantly High} = 26.69 + 2(1.25) \]

\[ \text{Significantly High} = 26.69 + 2.50 \]

\[ \text{Significantly High} = 29.19 \, \text{cm} \]

### Part 2: Identifying If 23.8 cm is Significantly Low, High, or Not Significant

Now, we'll check if 23.8 cm is significantly low, significantly high, or not significant.

- **Significantly Low**: 24.19 cm or lower
- **Significantly High**: 29.19 cm or higher

23.8 cm is less than 24.19 cm, so it is **significantly low**.

### Part 3: Answering the Choices

Given the results:

**Answer:**

**A.** The adult male foot length of 23.8 cm is significantly low because it is less than 24.19 cm.

---

Would you like more details on any step, or do you have any further questions?

Here are some related questions you might find helpful:
1. What is the "range rule of thumb" in statistics?
2. How do you calculate the mean and standard deviation from a data set?
3. Can foot length be normally distributed?
4. What other methods can identify outliers in a data set?
5. How does the standard deviation affect the spread of a data set?

**Tip:** Always double-check calculations when applying rules of thumb in statistics, especially when the context is sensitive to errors (e.g., medical studies).

Understand how to use the range rule of thumb in statistics to identify significantly low or high values. Solve a problem involving adult male foot lengths with a mean of 26.69 cm and a standard deviation of 1.25 cm. Determine if a foot length of 23.8 cm is significantly low, high, or not significant.

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