Question

A public interest group hires stu- dents to solicit donations by telephone. After a brief training period, students make calls to potential donors and are paid on a commission basis. Experience indicates that early on, these students tend to have only modest success and that 85% of them give up their jobs in their first two weeks of employment. The group hires 6 students, which can be viewed as a random sample.

1. What is the probability that at least 2 of the 6 will give up in the first two weeks?

2. What is the probability that at least 2 of the 6 will not give up in the first two weeks?

Answer 1

X ~ B ( n = 6 , P = 0.85 )

Part 1)

P(X = 2 ) = 0.0055
P(X = 3 ) = 0.0415
P(X = 4 ) = 0.1762
P(X = 5 ) = 0.3993
P(X = 6 ) = 0.3771

P ( X ≥ 2 ) = 0.9996

Part b)

X ~ B ( n = 6 , P = 0.15 )

P(X = 2 ) = 0.1762
P(X = 3 ) = 0.0415
P(X = 4 ) = 0.0055
P(X = 5 ) = 0.0004
P(X = 6 ) = 0

P ( X ≥ 2 ) = 0.2236