11.8 A mathematics placement test is given to all entering freshmen at a small college. A student who receives a grade below 35 is denied admission to the regular mathematics course and placed in a remedial class.

The placement test scores and the final grades for 20 students who took the regular course were recorded.

(a) Plot a scatter diagram.

(b) Find the equation of the regression line to predict course grades from placement test scores.

(c) Graph the line on the scatter diagram.

(d) If 60 is the minimum passing grade, below which placement test score should students in the future be denied admission to this course?

Placement Test Course Grade 50 53 35 41 35 61 40 56 55 68 65 36 35 11 60 70 90 79 35 59 90 54 80 91 60 48 60 71 60 71 40 47 55 53 50 68 65 57 50 79