Here's the solution to the provided problem:
If a student scores at the 50th percentile on the SAT, it means that 50% of the students scored lower and the other 50% scored higher. We can find the score using the following equation:
(1029 - x) / 205 = 0.5
Solving for x, we get:
x = 1029 - 205 * 0.5
x = 1029 - 102.5
x = 927.5
Therefore, a student’s SAT score of 928 would be the equivalent to scoring at the 50th percentile.
To find the equivalent ACT score, we first need the percentiles for the ACT scores. We can create a standard score distribution table by subtracting the mean from each score and dividing it by the standard deviation.
| | Standard Score | Percentile |
| --- | --- | --- |
| 27 | 0 | 99.5 |
| 26 | -1 | 97.2 |
| 25 | -2 | 94 |
| 24 | -3 | 89.8 |
| 23 | -4 | 85.1 |
| 22 | -5 | 78.6 |
| 21 | -6 | 70.2 |
| 20 | -7 | 61 |
| 19 | -8 | 51 |
| 18 | -9 | 40 |
| 17 | -10 | 30 |
| 16 | -11 | 20.6 |
| 15 | -12 | 11.5 |
| 14 | -13 | 3.4 |
| 13 | -14 | 0 |
The mean score is 22.7 and the standard deviation is 5, so the 50th percentile score is 22.7 - (5 * 0.02) = 22.7 - 0.1 = 22.6, or ACT score 23. Therefore, the equivalent ACT score for a student with a SAT score of 928 would be an ACT score of 23.
3. If a student has an SAT score