Consider a complex system with many independent components. In particular, suppose there are 50 such components. Suppose each component fails, independently, with probability 0.5. Suppose that the system can operate as long as the number of functioning components is greater than or equal to 30. Let N be the number of functioning components. Suppose that you want to know the probability that the system will be operational, namely that at least 30 of the components are working, i.e. P(N 30).

1. What is the distribution of the random variable N? Provide the expression for P(N 30) using the formula for the binomial probabilities (you do NOT need to simplify the expression).
2. Suppose you want to use the simulation methodology to estimate P(N 30). Let n be the number of simulations you run, and suppose you compute your estimate using the sample average from all the simulations. Use Chebyshev's inequality to compute how large n should be to ensure that your estimate is within 0.05 additive error of the true value with probability at least 0.95.