There are two major tests of readiness for college: the ACT and the SAT. ACT sco
ID: 3439044 • Letter: T
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 in recent years has been roughly Normal with mean = 20.9 and standard deviation = 4.8. SAT scores are reported on a scale from 400 to 1600. SAT scores have been roughly Normal with mean = 1026 and standard deviation = 209.
The SAT scores that make up the top 12% of all scores range from ( ) to 1600.
(Round your answer to the nearest whole number.)
Explanation / Answer
First, we get the z score from the given left tailed area. As
Left tailed area = 0.88
Then, using table or technology,
z = 1.174986792
As x = u + z * s / sqrt(n)
where
u = mean = 1026
z = the critical z score = 1.174986792
s = standard deviation = 209
Then
x = critical value = 1271.57224 = 1272 [ANSWER]