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

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:

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

About the SAT test, we have the following information:

Mean of 999. So

Standard deviation of 190. So

Jose scored 927. So

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

About the ACT test, we have the following information:

Mean of 15.6, so

Standard deviation of 3.9, so

We want to find the value o X when . So:

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