1. Suppose that repairs to an old machine are modelled with a Poisson distribution. It is estimated that the machine requires significant re- pairs once every 30 days. Recall that the Poisson distribution measures the probability of k events when the event frequency is A as k! (a) What is the probability that the machine requires more than 1 significant repair in the next 30 days? (b) Explain why the probability of no significant repairs in the next 45 days is e 3/2. (c) How many days are required for the probability of at least one significant repair to exceed 0.5