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?
Step 1 of 5
Here the data centre contains 1000 computer servers
The probability of failing each server is 0.003
Let X is no.of servers fail
Since ‘n’ is large and ‘p’ is small
The Binomial distribution will be converted to poisson distribution
The pmf of poisson distribution is P(X)=, X=0,1,2,..............
Hence XPoisson (3)