When the Scholastic Aptitude Test (SAT)now known as the Scholastic Assessment Testwas first developed, the idea was that each section of the test would have a mean of 500 and a standard deviation of 100. While the SAT is continually adjusted and readjusted to promote such a distribution, let us assume for this exercise that math scores on the SAT have a mean of 500 and a standard deviation of 100.

Suppose that a student receives a 465 on the math section of the SAT. What is the Z score that corresponds to this raw score? Interpret your answer from Question #1. What does this Z score represent in terms of the explanations provided in Chapter 6? What percentage of students who took the SAT scored below 465? What percentage scored above 465? What percentage of students who took the SAT scored between a 465 and 500? On the basis of your answers to the above questions, what percentile does a score of 465 correspond to? Suppose that a second student scored a 595 on the math portion of the SAT. Calculate the Z score associated with this raw score. What percentage of students scored above 595 on the math portion of the SAT? What is the percentile rank associated with a score of 595? What percentage of students who took the SAT posted scores between the two students discussed in this exercise? Assume for the moment that the first student who scored a 465 retook the SAT and posted a Z score of .35, representing a marked improvement over his or her previous score. What percentage of students who took the SAT posted scores between a Z score of .35 and a raw score of 595? Finally, suppose three siblings each take the SAT. The first two siblings post scores below the mean of 415 and 425 respectively. The third sibling however posts a score of 610. Calculate the proportion of students who took the SAT who either scored between 415 and 425 or above 610. What do we need to assume about the distribution of the SAT scores to create Z scores? Assuming the distribution of the SAT scores is normal, what can you say about the median, mean, and mode?