The Standard Normal Distribution · Exercise 50

During a certain year, 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 µ = 520 and standard deviation σ = 115.

(a) Calculate the z-score for an SAT score of 720. Interpret it using a complete sentence.
(b) What math SAT score is 1.5 standard deviations above the mean? What can you say about this SAT score?
(c) During a different year, the SAT math test had a mean of 514 and standard deviation 117. The ACT math test is an alternate to the SAT and is approximately normally distributed with mean 21 and standard deviation 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?

OpenStax, Introductory Statistics 2e · §6.1 The Standard Normal Distribution · Exercise 50