A data center contains 1000 computer servers. Each server has probability 0.003 of failing on a given day.
a. What is the probability that exactly two servers fail?
b. What is the probability that fewer than 998 servers function?
c. What is the mean number of servers that fail?
d. What is the standard deviation of the number of servers that fail?
Let X be the number of servers that fail. Then X is the number of successes in n = 1000 Bernoulli trials, each of which has success probability p = 0.003. The mean of X is np = (1000)(0.003) = 3. Since n is large and pis small, X ~ Poisson(3) to a very close approximation.
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