Question

Tradition says that an undergraduate student won’t graduate in four years if he/she walks underneath the Bell Tower at Purdue. Every time an undergraduate student walks past the tower, the probability that the student will walk underneath the tower is 0.08. Assume that each student is independent of any others.

a.) In one hour, 20 students walk past the tower, what is the probability that 4 of them will walk underneath the bell tower? Let S be the number of students who walk underneath the tower. Also state the distribution, parameter(s), and support of S.

b.) For the 20 students as described in part a)… Given that at least 2 students walk underneath the tower, what is the probability at most 3 students walk underneath it?

c.) 6 students have walked past the bell tower and none of these students walked underneath it. What is the probability that the next person will walk underneath the tower?

d.) 6 students have walked past the bell tower and none of these students walked underneath it. What is the probability that it takes more than 14 students (total) walking past the bell tower until the first student walks underneath it? State the distribution and parameter(s) you are using.

e.) What is the probability that the 10th student walking past the bell tower is the 2nd student to walk underneath the tower? Also state the distribution and parameter(s) that you are using.

f.) Find the expected value and standard deviation of the number of students who walk past the bell tower until the second one to walk underneath it.

Answer 1