SOLUTION: 1) There are 5 radar stations and the probability of a single radar station detecting an enemy plane is 0.65. What is the probability of 3 stations detecting an enemy plane? Round

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Question 627141: 1) There are 5 radar stations and the probability of a single radar station detecting an enemy plane is 0.65. What is the probability of 3 stations detecting an enemy plane? Round your answer to nearest hundredth.

2) The probability of a radar station detecting an enemy plane is 0.85. If 60 stations are in use, what is the expected number of stations that will detect an enemy plane? What is the standard deviation?
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
1. Let X = number of stations detecting an enemy plane
X~Binomial(5, 0.65)

2. The expected value of X if X~Binomial(n,p) is E(X) = np and the variance is Var(X) = npq where q=1-p. The standard deviation is the square root of Var(X).
expected number of stations that will detect an enemy plane
E(X) = 60(0.85) = highlight%2851%29
Standard deviation = sqrt%28%2860%29%280.85%29%280.15%29%29
= sqrt%287.65%29
= highlight%282.7659%29