A missile protection system consists of n radar sets operating independently, ea

Question

A missile protection system consists of n radar sets operating independently, each with a probability .9 of detecting a missile entering a zone that is covered by all of the units. (a). Let x be the number of radar sets which detect an incoming missile. How is X distributed? Be sure to explain your answer. (b). If n = 5 and a missile enters the zone, what is the probability that exactly 4 sets detect it? (c). If n = 5 and a missile enters the zone, what is the probability that at least 1 set detects it? (d). What is the expected proportion of missile sets that will detect an incoming missile when n = 20? (e). What is the standard deviation of the proportion of missile sets that will detect an incoming missile when n = 20?

Explanation / Answer

D) n = 20

expected value = n * p = 20 * 0.9 = 18

E) standard deviation = sqrt(n * p * (1-p))

= Sqrt(20 * 0.9 * 0.1)

= 1.342

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