Question: Complete the following statements.
a. In general, ____% of the values in a data set lie at or below the 58th percentile.
b. ____% of the values in a data set lie at or above the 44th percentile.
c. If a sample consists of 500 test scores, ____ of them would be at or below the 96th percentile.
d. If a sample consists of 500 test scores, ____ of them would be at or above the 4th percentile.
1. **State the problem:** We need to complete statements about percentiles and percentages of values in a data set.
2. **Recall the definition of percentile:** The $p$th percentile is the value below which $p\%$ of the data fall.
3. **Answer part a:** The 58th percentile means 58% of the values lie at or below it.
4. **Answer part b:** Values at or above the 44th percentile are $100\% - 44\% = 56\%$.
5. **Answer part c:** For 500 test scores, the number at or below the 96th percentile is $\frac{96}{100} \times 500 = 480$.
6. **Answer part d:** For 500 test scores, the number at or above the 4th percentile is $\frac{100 - 4}{100} \times 500 = 0.96 \times 500 = 480$.
**Final answers:**
a. 58%
b. 56%
c. 480
d. 480