1. Consider a binomial experiment with n = 10 and p=0.2

a.Compute f (0) (to 4 decimals).

b.Compute f (7) (to 4 decimals).

c.Compute P (x <2) (to 4 decimals).

d.Compute P(x>3) (to 4 decimals).

e.Compute E(x) (to 1 decimals).

f.Compute Var(x) and (to 2 decimals).

2. Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has aprobability of detecting a missile attack. Use the binomial probability distribution to answer the following questions.

a. What is the probability that a single detection system will detect an attack?

(to 2 decimals)

b. If two detection systems are installed in the same area and operate independently, what is the probability that at least one of the systems will detect the attack?

(to 4 decimals).

c. If three systems are installed, what is the probability that at least one of the systems will detect the attack?

(to 4 decimals)

3.A university found that40%of its students withdraw without completing the introductory statistics course. Assume that20students registered for the course.

a.Compute the probability that 2or fewer will withdraw (to 4 decimals).

b.Compute the probability that exactly 4will withdraw (to 4 decimals).

c.Compute the probability that more than3will withdraw (to 4 decimals).

d.Compute the expected number of withdrawals.