Hures of Relative Standing Use the range rule of thumb to identify the values that are significantly low, the values that are signficantly high, and the values that are neither significantly low nor significantly high. \( 62.98 \%, 8.82 \) of 14 points A test is used to assess readiness for college. In a recent year, the mean test score was 21.5 and the standard deviation was 4.6 . Identify the test scores that are significantly low or signific \( 3,3.3 .9 \) What test scores are significantly low? Select the correct answer below and fill in the answer box(es) to complete your choice. A. Test scores that are greater than \( \square \). (Round to one decimal place as needed.) B. Test scores that are between \( \square \) and \( \square \). (Round to one decimal place as needed, Use ascending order.) C. Test scores that are less than \( \square \). (Round to one decimal place as needed.)

To determine which test scores are **significantly low**, **significantly high**, or **neither**, we'll use the **Range Rule of Thumb**. This rule states that: - **Most** of the data (approximately 95%) falls within **two standard deviations** of the mean. - **Significantly high** values are those **more than two standard deviations above** the mean. - **Significantly low** values are those **more than two standard deviations below** the mean. Given: - **Mean (\( \mu \))** = 21.5 - **Standard Deviation (\( \sigma \))** = 4.6 ### Step 1: Calculate Two Standard Deviations 1. **Two standard deviations above the mean**: \[ \mu + 2\sigma = 21.5 + (2 \times 4.6) = 21.5 + 9.2 = 30.7 \] 2. **Two standard deviations below the mean**: \[ \mu - 2\sigma = 21.5 - (2 \times 4.6) = 21.5 - 9.2 = 12.3 \] ### Step 2: Categorize the Test Scores Based on these calculations: - **A. Test scores that are greater than \( 30.7 \)**: - **Significantly High** - **B. Test scores that are between \( 12.3 \) and \( 30.7 \)**: - **Neither Significantly Low nor High** - **C. Test scores that are less than \( 12.3 \)**: - **Significantly Low** ### Filled-in Answers: **A. Test scores that are greater than** \( \boxed{30.7} \). **B. Test scores that are between** \( \boxed{12.3} \) **and** \( \boxed{30.7} \). **C. Test scores that are less than** \( \boxed{12.3} \). ### Summary: - **Significantly Low**: Scores **less than 12.3** - **Neither**: Scores **between 12.3 and 30.7** - **Significantly High**: Scores **greater than 30.7** This categorization helps in identifying students who may need additional support (significantly low) or those who are excelling (significantly high), while the majority fall into the "neither" category.