In the very large lecture class CHEM 115, 85% of students passed the first exam. Joe did poorly and wants to start a study group for students who failed the first test, with 10 students (including himself) in the group. Because of FERPA privacy laws, the CHEM 115 instructor is not allowed to tell Joe who failed the first exam. Instead, Joe must ask students in CHEM 115 until he finds 9 other students who failed the first exam to join him in his study group. Let F be the number of students Joe must ask before he fills his study group. (Assume all failing students agree to be in the student group when asked.)
a) What is the distribution and parameters for F?
b) What is the variance of number of students Joe will ask to fill his study group?
c) What is the probability it takes him between 17 and 20 (inclusive) students to fill his study group?
d) Given it takes him between 17 and 20 students (inclusive) to fill his study group, what is the probability it takes either 18 or 19 students to fill his study group?