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. Part (a)
Calculate the z-score for an SAT score of 710. Interpret it using a complete sentence. (Round your answer to two decimal places.)
The z-score is ___. The exam score of 710 is ___ standard deviations (above/below) the mean of 520.
Part (b)
What math SAT score is 1.4 standard deviations above the mean? What can you say about this SAT score? (Enter your answer to one decimal place.)
The score SAT score is . This score is 1.4 standard deviations (above/below) the mean.
Part (c)
For 2012, 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 33, who did better with respect to the test they took? (Round your answers to two decimal places.)
The z-score for an SAT score of 700 is . The z-score for an ACT score of 33 is . Therefore, the student who took the (SAT/ACT) did better, because that person has a (higher/lower) z-score.