Continuous Probability Distributions

In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean = 520 and standard deviation = 115.

1. Calculate the z-score for an SAT score of 720. Interpret it using a complete sentence.

2. What math SAT score is 1.5 standard deviations above the mean? What can you say about this SAT score?

3. For 2012, the SAT math test had a mean of 514 and a standard deviation of 117. The ACT math test is an alternative to the SAT and is approximately normally distributed with a mean of 21 and a standard deviation of 5.3. If one person took the SAT math test and scored 700 and a second person took the ACT math test and scored 30, who did better with respect to the test they took?