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 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. Exercises 1.124 through 1.133 are based on this information.

1.124 Compare an SAT score with an ACT score. Jessica scores 1830 on the
SAT. Ashley scores 27 on the ACT. Assuming that both tests measure the same thing, who has the
higher score? Report the z-scores for both students.
1.125 Make another comparison. Joshua scores 16 on the ACT. Anthony scores 1050
on the SAT. Assuming that both tests measure the same thing, who has the higher score? Report the
z-scores for both students.
1.126 Find the ACT equivalent. Jorge scores 2090 on the SAT. Assuming that both tests
measure the same thing, what score on the ACT is equivalent to Jorge’s SAT score?
1.127 Find the SAT equivalent. Alyssa scores 30 on the ACT. Assuming that both tests
measure the same thing, what score on the SAT is equivalent to Alyssa’s ACT score?

Answer 1

Solution:

Given:

ACT :

The distribution of ACT scores is approximately Normal with mean μ = 21.5 and standard deviation σ = 5.4.

SAT:

The distribution of SAT scores is approximately Normal with mean μ = 1498 and standard deviation σ =316.

1.124 Compare an SAT score with an ACT score. Jessica scores 1830 on the SAT. Ashley scores 27 on the ACT. Assuming that both tests measure the same thing, who has the higher score?

Find z score for  Jessica scores 1830 on the SAT.

Now find z score for  Ashley scores 27 on the ACT.

Since z score for Jessica scores 1830 on the SAT is 1.05 which is more than z score for  Ashley scores 27 on the ACT which is 1.02,  Jessica has the higher score.

1.125 Make another comparison. Joshua scores 16 on the ACT. Anthony scores 1050 on the SAT. Assuming that both tests measure the same thing, who has the higher score?

Now find z score for  Joshua scores 16 on the ACT.

Find z score for  Anthony scores 1050on the SAT.

Since z score for Joshua scores 16 on the ACT is -1.02 is greater than that of  Anthony scores 1050on the SAT, Joshua  has the higher score.

1.126 Find the ACT equivalent. Jorge scores 2090 on the SAT. Assuming that both tests measure the same thing, what score on the ACT is equivalent to Jorge’s SAT score?

Find z score for  Jorge scores 2090on the SAT.

Now use following formula to find x value (ACT score) :

1.127 Find the SAT equivalent. Alyssa scores 30 on the ACT. Assuming that both tests measure the same thing, what score on the SAT is equivalent to Alyssa’s ACT score?

find z score for   Alyssa scores 30 on the ACT.

Now use following formula to find x value (SAT score) :

( Round answer to specified number of decimal places)