There are two major tests of readiness for college: the ACT and the SAT. ACT sco
ID: 3053395 • 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 µ = 20.9 and standard deviation s = 4.8. SAT scores are reported on a scale from 400 to 1600. SAT scores have been roughly Normal with mean µ = 1026 and standard deviation s = 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 1280 on the SAT. What is her percentile (± 1)?
Explanation / Answer
P(X < A) = P(Z < A - µ)/s)
For SAT score, mean µ = 1026 and standard deviation s = 209
SO, P(X < 1280) = P(Z < (1280-1026)/209)
= P(Z < 1.22)
= 0.8888 (from standard normal distribution table)
= 88.88 percentile
Tanya's percentile is 88.88