1. Verbal SAT scores follow approximately a normal distribution and math SAT scores also follow approximately a normal distribution.
a. A particular freshman student at Discrete College has a standardized verbal
SAT of z=-1.3 and a standardized math SAT test score of z=2.0.
Explain what these values tell you.
b. Another freshman at Discrete College has a standardized math SAT test score of 1.5. How does the student in (a) compare to this student?
c. Suppose you also know that the mean math SAT score for freshman students at Discrete College is 547 and the standard deviation is 74. What can you say about the math SAT test score of the student with a standardized math SAT score of 2.0?
d. Use the empirical rule to find an interval of values within which approximately 68 percent of the freshmen math SAT scores at Discrete College fall.
e. Use the empirical rule to find an interval of values within which approximately 95 percent of the freshman math SAT scores at Discrete College fall.
2. Biff teaches a section of Discrete Structures, and on Exam 01 his students' scores were approximately normally distributed with a mean of 78 and a standard deviation of 6. Bubba teaches a different section of Discrete Structures, and on Exam 01 his students' scores were also approximately normally distributed, with a mean of 74 and a standard deviation of 10.
Two students, one from each section, scored 92. Calculate the z-score for each student, and then make a claim as to who performed better on the exam.