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

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

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 = (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 = (X - \mu)/(\sigma) = (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 = (X - \mu)/(\sigma)`

`-0.38 = (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.