Answer :
the equivalent ACT score for Jorge's SAT score of 1400 is approximately 19.82.
To find the equivalent ACT score for Jorge's SAT score of 1400, we need to standardize Jorge's SAT score and then convert it to an ACT score using the mean and standard deviation of the ACT scores.
First, let's standardize Jorge's SAT score:
[tex]\[ Z = \frac{{X - \mu}}{{\sigma}} \][/tex]
Where:
- X = Jorge's SAT score = 1400
- [tex]\( \mu \)[/tex] = Mean SAT score = 1498
- [tex]\( \sigma \)[/tex] = Standard deviation of SAT scores = 316
[tex]\[ Z = \frac{{1400 - 1498}}{{316}} = \frac{{-98}}{{316}} \approx -0.3101 \][/tex]
Now, we'll use the standardized score to find the equivalent ACT score:
[tex]\[ Z = \frac{{X - \mu}}{{\sigma}} \][/tex]
Where:
- X = Equivalent ACT score
- [tex]\( \mu \)[/tex] = Mean ACT score = 21.5
- [tex]\( \sigma \)[/tex] = Standard deviation of ACT scores = 5.4
[tex]\[ -0.3101 = \frac{{X - 21.5}}{{5.4}} \]\[ -0.3101 \times 5.4 = X - 21.5 \]\[ -1.6754 = X - 21.5 \]\[ X = -1.6754 + 21.5 \]\[ X \approx 19.8246 \][/tex]
So, the equivalent ACT score for Jorge's SAT score of 1400 is approximately 19.82.
The probable question maybe:
There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores is approximately Normal with mean μ = 21.5 and standard deviation σ = 5.4. SAT scores are reported on a scale from 600 to 2400. The distribution of SAT scores is approximately Normal with mean μ = 1498 and standard deviation σ = 316.
Jorge scores 1400 on the sat. assuming that both tests measure the same thing, what score on the act is equivalent to Jorge's sat score?
