Question: SAT versus ACT

There are two major tests of readiness for college: the SAT and the ACT. While ACT are reported on a scale from 1 to 36, SAT scores until recently was reported on a scale from 400 to 1600. The scores of

ACT has a distribution that follows: N(20.9, 4.8) and SAT follows a distribution of N(1026, 209).

Answer the following questions:

(a) Maria scores 28 on the ACT. Assuming that both tests measure the same thing, what score on the SAT is equivalent to Maria's ACT score?

(b) Tonya scores 1318 on the SAT. What is her percentile?

(c) The quartiles of any distribution are the values with cumulative proportion 0.25, 0.50, and 0.75. What are the quartiles of the distribution of the ACT scores?

(d) The quintiles of any distribution are the values with cumulative proportion 0.20, 0.40, 0.60, and 0.80. What are the quintiles of the distribution of SAT scores?

(e) What SAT scores make up the 90th percentile?

(f) How well must Abigail do on the ACT in order to place in the top 1 percent?