Based on recent results, scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312. Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1. Assume that the two tests use different scales to measure the same aptitude.
a. If someone gets an SAT score that is in the 95th percentile, find the actual SAT score and the equivalent ACT score.
b. If someone gets an SAT score of 2100, find the equivalent ACT score.