Question: Verbal SAT test scores follow approximately a normal distribution and math

SAT test scores also follow approximately a normal distribution.

(a) A particular freshman student at a certain college has a standardized verbal SAT test score of z = –1.3 and a standardized math SAT test score of z = 2.0. Explain what these values tell you.

(b) Another freshman has a standardized math SAT test score of 1.5. How does the student described in part a of this exploration compare to this student?

(c) Suppose you also know that the mean math SAT test score for freshmen students at this 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 test 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 this college fall.

(e) Use the empirical rule to find an interval of values within which approximately 95 percent of the freshmen math SAT scores at this college fall.