BINOMIAL AND POISSON EXERCISES POISSON DISTRIBUTION A bank receives on average 6 fake checks per day, calculate the probability that five fake checks are received per day. Suppose that the average number of imperfections in a thin copper wire is 2.3 imperfections per millimeter. Determine the probability of 2 imperfections in one millimeter. Messages arriving at a computer used as a server do so according to a Poisson distribution with an average rate of 0.1 messages per minute. Determines the probability that at most 2 messages arrive in one minute. The number of punctures in the tires of a certain commercial vehicle has an average of 0.3 per 50,000 kilometers. If the vehicle travels 100,000 kilometers, calculate the probability that it has fewer than 3 punctures. BINOMIAL DISTRIBUTION Exercise 1.-30% of a certain town watches a contest on television. From the contest, 10 people from the town chosen at random are called by phone. Calculate the probability that, among the 10 people, they were watching the program: a) More than eight people b) Some of the ten people c) Less than 5 people Exercise 2.- The head of human resources of a company performs a ten-item test on applicants for a position, with each item having four possible answers, of which only one is correct. Assuming that the applicants have the same probability of responding. It is asked to find the probabilities for the applicant: a) Answer all the items incorrectly b) Answer at least four items correctly c) Answer between four and six items correctly d) Answer all the items correctly e) Answer less than three items correctly.