1.   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?

2.   One out of every 5000 individuals in a population carries a certain defective gene. A random sample of 1000 individuals is studied.

a.   What is the probability that exactly one of the sample individuals carries the gene?

b.   What is the probability that none of the sample individuals carries the gene?

c.   What is the probability that more than two of the sample individuals carry the gene?

d.  What is the mean of the number of sample individuals that carry the gene?

e.  What is the standard deviation of the number of sample individuals that carry the gene?