You work for a company that has 46 identical machines operating to produce Justin Beiber CDs. These machines operate as long as certain components are working. There are three components in particular, call them A, B & C. A machine operates as long as C & A or C & B are working. Specifications from the manufactures tell you that the failure time of each part is normally distributed as follows:
A's failure time ~ N (μ=9 months, σ2=8 months)
B's failure time ~ N (μ=13 months, σ2=5 months)
C's failure time ~ N (μ=24 months, σ2=9 months)
Assume that the parts failure times are independent. Your boss asks you to find how many machines can the company expect to fail in a year and the probability that at least 10 machines fail in a year.