Suppose SAT scores in a particular year are (approximately) normally distributed with a mean of 1,450 and a standard deviation of 290. Additionally, suppose ACT scores that same year are also (approxi- mately) normally distributed with a mean of 20 and a standard deviation of 4.5. Use this information to answer each part below.
(a) A student is applying for college and is required to submit their results from one of the two above mentioned tests. If they scored a 1610 on the SAT and a 24 on the ACT, which grade is better? Use z-scores to compare the two tests. (b) Another student took the same two tests and scored a 1,900 on the SAT and a 12 on the ACT. Would either of these scores be considered unusual? Use z-scores to confirm your answer(s).
Note: A z-score is considered to be unusual if it is more than two standard deviations away from the mean.