There are two major tests of readiness for college: the ACT and the SAT. ACT sco
ID: 3159136 • 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.
Reports on a student's ACT or SAT usually give the percentile as well as the actual score. The percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one.
Tanya scores 1317 on the SAT. What is her percentile (± 1)? %
Explanation / Answer
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 1317
u = mean = 1026
s = standard deviation = 209
Thus,
z = (x - u) / s = 1.392344498
Thus, using a table/technology, the left tailed area of this is
P(z < 1.392344498 ) = 0.918090949 = 0.92 = 92nd percentile [ANSWER: 92]