Measures of Relative Standing \( K \quad \begin{array}{l}\text { Question 4, 3.3.11 } \\ \text { Part } 1 \text { of } 3\end{array}, \begin{array}{l}\text { In designing a work desk, it is found that males have sitting knee heights with a mean of } 21.3 \text { in. and a standard deviation of } 1.1 \text { in. (based on data from the Department of Transportation). Use } \\ \text { thumb to identify (a) the values that are significantly low, (b) the values that are significantly high, and (c) the values that are neither significantly low nor significantly high. }\end{array} \)

To determine which sitting knee heights are significantly low, significantly high, or neither, we'll use the **standard deviation method**, a common "rule of thumb" in statistics. Given: - **Mean (\( \mu \))** = 21.3 inches - **Standard Deviation (\( \sigma \))** = 1.1 inches **Step 1: Determine the Thresholds** A common approach is to consider values **more than 2 standard deviations** away from the mean as significantly low or high. - **Significantly Low Threshold**: \( \mu - 2\sigma = 21.3 \, \text{in} - (2 \times 1.1 \, \text{in}) = 19.1 \, \text{in} \) - **Significantly High Threshold**: \( \mu + 2\sigma = 21.3 \, \text{in} + (2 \times 1.1 \, \text{in}) = 23.5 \, \text{in} \) **Step 2: Categorize the Values** - **(a) Significantly Low Values**: Any knee height **less than 19.1 inches** is considered significantly low. - **(b) Significantly High Values**: Any knee height **greater than 23.5 inches** is considered significantly high. - **(c) Neither Significantly Low Nor High**: Knee heights **between 19.1 inches and 23.5 inches** are neither significantly low nor high. **Summary:** - **Significantly Low**: \( < 19.1 \) inches - **Significantly High**: \( > 23.5 \) inches - **Neither**: \( 19.1 \) inches to \( 23.5 \) inches This categorization helps in designing work desks that accommodate the majority of users while identifying outliers that may require special consideration.