In one of the author’s statistics classes, 27 students responded anonymously to the following two questions: “How many friends did you have during your senior year in high school? How many of those people are you still in touch with and consider to be friends?” For each student, the author computed the friend-retention rate (FRR), which is the percentage of the student’s high-school friends that the student was still friends with. The distribution of FRRs is unimodal and symmetric with mean 42.7% and standard deviation 20.5%.
a. Two students had no friends in high school. Explain why it makes sense that the author did not compute FRRs for those two students.
b. Out of the 25 FRRs, approximate how many were between 22.2% and 63.2%.
c. Out of the 25 FRRs, approximate how many were between 1.7% and 83.7%.
d. One student was still friends with all of his or her high school friends. What is that student’s FRR? Is that an unusual FRR? Explain.
e. From reading the opening paragraph of this exercise, a student concludes that the mean FRR for all college students is 42.7%. What would you tell the student?