For students who graduated from high school in 2013, the ACT math scores are approximately normally distributed with mean 20.9 points and standard deviation 5.3 points.
a. If a freshman at Thomas More College (TMC) scored 17 points on the math sections of the ACT, the student was required to take a one-semester beginning algebra course. What is the z-score of 17 points? Why does it make sense that your result is negative?
b. If a freshman at TMC scored at most 16 points on the math sections of the ACT, the student was required to take a two-semester beginning algebra course. What proportion of students who took the ACT scored at most 16 points?
c. A student says your result in part (c) is the proportion of all TMC students who had to take the two-semester beginning algebra course. What would you tell the student?