There are two major tests of readiness for college, the ACT and the SAT. ACT sco
ID: 3275050 • 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 for more than 1 million students in a recent high school graduating class was roughly normal with mean = 20.8 and standard deviation = 4.8. 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 = 1026 and standard deviation = 209.
How well must Abigail do on the SAT in order to place in the top 16% of all students? (Round your answer to the nearest whole number.)
Please show steps and explain.
Explanation / Answer
For SAT scores, mean = 1026 and std. dev. = 209
z-value associated with 0.16 is 0.9945 (this value can be determined using standard z table and as we are concerned with top %, we consider right tail)
Using central limit,
z = (xbar - mu)/sigma
xbar = 0.9945*209 + 1026 = 1233.85
Hence 1234 should be the SAT score in order to place Abigail in the top 16% of all students.