Individuals are sometimes classified according to where they fall in a distribution. For example, if a college applicant's GPA is in the top 2% of their applicant pool, they are awarded a scholarship. Another example might be if a cat's weight is in the lowest 10% for their breed, this may mean the cat is undernourished or in need of a special diet. In the next few questions, we will explore this idea more.

(14) When Dr. Shah finishes final grades for her statistics class each semester, she recommends the top 5% of students to be peer tutors in future semesters. In her most recent class, the mean final grade was a 79% with a standard deviation of 5.8%. What is the cutoff score Dr. Shah will use to recommend peer tutors this semester? (3 points)

(15) Students who score in the bottom 20% of ACT scores for their peer group are offered a free ACT prep course prior to re-taking the test. Last autumn, the mean ACT score for the group taking the test was a 29 with a standard deviation of 4.2. What ACT score is the cutoff below which students will be offered the free prep course? (3 points)

(16) Any 3^rd grader scoring in the 95^th percentile or higher on their reading test in September is put into the highest reading group for the year. This group moves faster through reading activities and is offered more opportunities to select and read their own books. In September 2022, Mr. Finch's students averaged a 65% on the reading test with a standard deviation of 7%. What is the cutoff score for determining which students will go into the highest reading group? (3 points)

(17) The scenarios in Questions 14 - 16 use one value to make decisions about placing individuals into groups. In at least few sentences, discuss whether you think basing these decisions on one value is equitable - that is, does everyone in the group have the same opportunities? (6 points)