A group of adult males has foot lengths with a mean of 27.08 cm and a standard deviation of 1.35 cm . Use the range rule of thumb for identifying significant values to identify the lim
separating values that are significantly low or significantly high. Is the adult male foot length of 23.9 cm significantly low or significantly high? Explain.

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UpStudy AI · Accepted Answer

To determine whether a foot length of **23.9 cm** is significantly low or high among adult males, we can apply the **range rule of thumb**. This rule provides a simple way to identify outliers by using the mean and standard deviation of the data set.

### **Range Rule of Thumb:**
- **Most** data points fall within **two standard deviations** from the mean.
- **Significantly low** values are typically more than **two standard deviations below** the mean.
- **Significantly high** values are typically more than **two standard deviations above** the mean.

### **Given Data:**
- **Mean (µ):** 27.08 cm
- **Standard Deviation (σ):** 1.35 cm

### **Calculating the Limits:**
1. **Lower Limit (Significantly Low):**
   $$
   \text{Mean} - 2 \times \text{Standard Deviation} = 27.08\ \text{cm} - 2 \times 1.35\ \text{cm} = 27.08\ \text{cm} - 2.7\ \text{cm} = 24.38\ \text{cm}
   $$
   
2. **Upper Limit (Significantly High):**
   $$
   \text{Mean} + 2 \times \text{Standard Deviation} = 27.08\ \text{cm} + 2 \times 1.35\ \text{cm} = 27.08\ \text{cm} + 2.7\ \text{cm} = 29.78\ \text{cm}
   $$

### **Interpretation:**
- **Significantly Low:** Foot lengths **below 24.38 cm**
- **Significantly High:** Foot lengths **above 29.78 cm**

### **Assessment of 23.9 cm:**
- **23.9 cm** is **below** the lower limit of **24.38 cm**.
- This places the foot length **more than two standard deviations below** the mean.
  
### **Conclusion:**
A foot length of **23.9 cm** is **significantly low** for adult males based on the range rule of thumb.

**Summary:**
Using the range rule, foot lengths below 24.38 cm or above 29.78 cm are significantly low or high. Since 23.9 cm is below 24.38 cm, it is significantly low.
A foot length of 23.9 cm is significantly low for adult males.

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