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Binomial and Poisson Distributions Solve the following problems: A. Binomial 1. If it's true that 85% of all industrial accidents can be prevented by paying strict attention to safety regulations, find the probability that 4 of 7 industrial accidents can thus be prevented, using the formula for binomial distribution. 2. In a given city, , medical expenses are given the, reason, for fun of all personal Jankoentries . What is the probability that medical expenses will be given as the reason for four of the next personal bankruptcies filed by the city? 3. If the probability is 0.60 that a person traveling in a certain airline will pay extra to see a movie, what is probability that only 3 of 6 persons travelling on this airline will pay an extra to see a movie. + It is known that 20% of all persons given a certain "medication" get very drowsy within 2.5 minutes. Find the probabilities that among 15 persons given the medication: a) At most two will get very drowsy within 2 minutes b) At least 5 get very drowsy within 2 minutes B. Poisson 1. Between 7 p.m. and 8 p.m., the country's leading phone directory receives calls at the rate of 3 per minute. Assume that the calls arrive at random points in time. Determine the probability that: a) 6 calls arrive in a randomly selected minute b) 8 calls arrive in a randomly chosen 2-minute period. . Records show that the probability that a car will have a flat tire while driving through a certain tunnel is 0.00006. Use the Poisson approximation to the binomial distribution to find the probability that at least 1 of 5,000 cars passing through this tunnel will have flat tires. 3. If a bank receives an average /= 9 bad checks per day, what is the probability that it will receive 6 bad checks on a given day? The number of accidents in a randomly selected week at a factory can be modeled by a Poisson distribution with a mean 3. Find the probability that there are more than two accidents in a randomly chosen week The number of customers per hour entering a jeweler's shop has a Poisson distribution. For the first hour after opening, the mean is 2 costumers per hour and for the next 3 hours, the mean is 3 customers per hour. Find the probability that there are between 4 and 6 (inclusive) costumers entering the shop in the first four hours. 6. Independently for each page of a printed book, the number of errors occurring has a Poisson distribution with mean 0.2. Find the probabilities that: a) The first page will contain no error b ) Four of the first five pages will contain no errors c) The first error will occur on the third page