10. Let X be a Poisson random variable where P(3) - 2-P(4). Find P(5). A bank has one automatic teller machine. Customers arrive at the machine at a rate of 17 per hour. Assuming that customers arrive according to a Poisson distribution, find the probability that there will be exactly 15 customers in the next hour. 12. A biased coin with P(heads) - .65 is flipped 8 times. Let the random variable X be the number of heads observed. (a) What is the p.m.f. of X? (b) Find P(X = 5) It has been verified that an ambulance service responds to 85% of its calls within 10 Minutes, i.e. the probability of a response time of less than or equal to 10 minutes is 85% What is the probability that (a) fewer than 12 of the next 20 calls are responded to within 10 minutes? (b) more than 2 of the next 10 calls require more than 10 minutes? 14. A component in a complex space shuttle system has a failure rate of 75%. How many of these components should be installed so that the probability that at least one of those installed will function is greater than 99%