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 are 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 SAT scores are approximately Normal with mean μ = 1498 and standard deviation σ = 316.

What SAT scores make up the top 14% of all scores? (Round your answer to the nearest whole number.)

Scores blank  and higher make up the top 14% of all scores.

Answer 1

top 14% means a score that is above bottom 86% of scores

z score for 86th percentile is 1.08

mean and standard deviation for SAT scores are μ = 1498 and σ = 316.

hence,

Scores 1839 and higher make up the top 14% of all scores.