A production line produces a variable number N of times each day. Suppose each item produced has the same probability p of not conforming to manufacturing standards. If N has a Poisson distribution with mean λ, then the number of nonconforming items in one day's production Y has a Poisson distribution with mean λ p. The average number of resistors produced by a facility in one day has a Poisson distribution with mean 100. Typically, 5% of the resistors produced do not meet specifications.
a Find the expected number of resistors not meeting specifications on a given day.
b Find the probability that all resistors will meet the specifications on a given day.
c Find the probability that more than five resistors fail to meet specifications on a given day.