Question

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 for more than 1 million students in a recent high school graduating class was roughly normal with mean μ = 15.6 and standard deviation σ = 3.9. SAT scores are reported on a scale from 400 to 1600. The SAT scores for 1.4 million students in the same graduating class were roughly normal with mean μ = 999 and standard deviation σ = 190.Jose scores 927 on the SAT. Assuming that both tests measure the same thing, what score on the ACT is equivalent to Jose's SAT score

Answer 1

Answer:

An ACT score of 14.118 is equivalent to Jose's SAT score.

Step-by-step explanation:

The ACT equiavalent to Jose's SAT score is going to be ACT grade with the same z-score as Jose's SAT grade.

The z-score formula is given by:

$Z = \frac{X - \mu}{\sigma}$

In which: X is Jose's grade, $\mu$ is the mean value of all the grades and $\sigma$ is the standard deviation of the grades.

About the SAT test, we have the following information:

Mean of 999. So $/mu = 999$

Standard deviation of 190. So $\sigma = 190$

Jose scored 927. So $X = 927$

The z-score of Jose's SAT grade is:

$Z = \frac{X - \mu}{\sigma} = \frac{927 - 999}{190} = -0.38$

About the ACT test, we have the following information:

Mean of 15.6, so $\mu = 15.6$

Standard deviation of 3.9, so $\sigma = 3.9$

We want to find the value o X when $Z = -0.38$. So:

$Z = \frac{X - \mu}{\sigma}$

$-0.38 = \frac{X - 15.6}{3.9}$

$X - 15.6 = -1.482$

$X = 14.118$

An ACT score of 14.118 is equivalent to Jose's SAT score.