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3.29 A train is made up of 50 railroad cars. Each car may need Let X be the total number of cars in the train that need service. service with probability 0.05 a) Find the mean and standard deviation of X b) Find the probability that no cars need service c) Find the probability that at least two cars need service.

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Answer #1

We use poisson distribution p(X-x)--with the parameter λ = np = (50)(0.05)= 2.5 (a) mean = λ = 2.5 and standard deviation-M-J25-1 .5811 2.5_.-2.5 0.0821 0! (c)p(x2 2) 2.5 1! 1-(0.0821 +0.2052) e2 32.50e 32.5 0! 0.7127

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