The Standard Normal Distribution · Exercise 50
In 2005, 1,475,623 students heading to college took the SAT exam. 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) For 2012, the SAT math test had a mean of 514 and standard deviation 117. The ACT math test is an alternative to the SAT math test, 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 that each person took?
OpenStax, Statistics · §6.1 The Standard Normal Distribution · Exercise 50
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