Question 1181511
Here's the solution:

**1. Completed Table:**

To find the lower boundaries (LB), subtract 0.5 from each lower class limit.

| NCAE Scores | f (frequency) | LB    |
|-------------|---------------|-------|
| 39-41       | 6             | 38.5  |
| 36-38       | 7             | 35.5  |
| 33-35       | 9             | 32.5  |
| 30-32       | 13            | 29.5  |
| 27-29       | 22            | 26.5  |
| 24-26       | 10            | 23.5  |
| 21-23       | 9             | 20.5  |
| 18-20       | 7             | 17.5  |
| 15-17       | 8             | 14.5  |
| 12-14       | 4             | 11.5  |
| 9-11        | 2             | 8.5   |
| 6-8         | 1             | 5.5   |
| 3-5         | 1             | 2.5   |

**2. 3rd Quartile (Q3), 72nd Percentile (P72), and 8th Decile (D8):**

First, find the cumulative frequency (cf):

| NCAE Scores | f  | cf |
|-------------|----|----|
| 39-41       | 6  | 88 |
| 36-38       | 7  | 82 |
| 33-35       | 9  | 75 |
| 30-32       | 13 | 66 |
| 27-29       | 22 | 53 |
| 24-26       | 10 | 31 |
| 21-23       | 9  | 21 |
| 18-20       | 7  | 12 |
| 15-17       | 8  | 5  |
| 12-14       | 4  | 1  |
| 9-11        | 2  | 1  |
| 6-8         | 1  | 1  |
| 3-5         | 1  | 1  |

*   **Q3:** Q3 is the 75th percentile.  (75/100) * 88 = 66. The 66th value falls in the 33-35 class.

    Q3 = LB + [( (75/100) * N - cf_below ) / f_class ] * class_width
    Q3 = 32.5 + [ (66 - 53) / 9 ] * 3
    Q3 = 32.5 + 4.33 = 36.83

*   **P72:** (72/100) * 88 = 63.36. The 63.36th value falls in the 30-32 class.

    P72 = 29.5 + [(63.36 - 53) / 13] * 3
    P72 = 29.5 + 2.41 = 31.91

*   **D8:** (8/10) * 88 = 70.4. The 70.4th value falls in the 33-35 class.

    D8 = 32.5 + [(70.4 - 53) / 9] * 3
    D8 = 32.5 + 5.8 = 38.3

**3. Percentile Rank of Dennis and Christine:**

*   **Dennis (score 32):** Dennis's score falls in the 30-32 class.

    Percentile Rank = [ (cf_below + 0.5 * f_class) / N ] * 100
    Percentile Rank = [ (53 + 0.5 * 13) / 88 ] * 100
    Percentile Rank = [ (53 + 6.5) / 88 ] * 100
    Percentile Rank = (59.5 / 88) * 100 ≈ 67.61

*   **Christine (score 23):** Christine's score falls in the 21-23 class.

    Percentile Rank = [ (21 + 0.5 * 9) / 88 ] * 100
    Percentile Rank = [ (21 + 4.5) / 88 ] * 100
    Percentile Rank = (25.5 / 88) * 100 ≈ 28.98