Let x be a Poisson random variable with y = 6.5. Find the probabilities forx using Table 2. [Round your answers to three decimal places.) An outbreak of E. coriintecb'ons in July of 2017 occurred in southwestern utah. with a dozen people sick. and the conrmed deaths of two children. E. cah lrlfectlnns and outbreaks have been on the rise since 2009, reaching an incidence rate of 2.35 cases per 100,000 persuns.T children under the age or live have a higher incidence ratei7.BS cases per 100,000. Using the rate af2.BE cases per 100,000, evaluate the following probabilities. (Round your answers to three decimal places.) (a) what is the probability that at most one outbreek per 100,000 is reported across the united states this year" \\:| (b) what is the probability that more than four outbreaks per 100,000 are reported across the United states this year? \\:| Let x be a binomial random variable with n = 20 and p = 0.05. Calculate pm) and p{1) using Table 1 to obtain the exact binomiai probability. (Round your answers to three decimal pieces.) mm = |:l PEI) = |:l Calculate pm) and p{1) using the Poisson approximation. (Round your answer to three decimal piaces.) pm: : |:l m1) = |:l Compare your results. Is the approximation accurate? 0 Yes the approximation is reasonably accurate. In general, the probabilities from the Poisson approximao'on are all well within 0.05 of the exact probabilities from the binomial distribution. 0 No the approximation is not accurate. At least one the differences between the probabilities from the Poisson approximation and the exact probabil ies from the binomial distribution is much greater than 0.05. The number of bankruptcies led in the district court has a Poisson distributan with an avelage of 5.5 per week. (a) what is the probability that there will be no bankruptcy lings during a given week? [Round your answer to three decimal places.) E (b) What is the probability that there will be at least one bankruptcy ling during a given week? (Round your answer to three decimal places.) E (c) Within what limits does Tchebyshef'f's Theorem suggest you would expect to see the number of bankruptcy lings per week at least 58.88% of the time"j (Round your answer up to the nearest whole number.) \fThe increased number uf small commuter planes in major airpcns has heightened concern over air safety. An eastern airport has recorded a monthly average 0F two near misses on landings and taltecrrs in the past 5 years. (Reund yuur answers to three decimal places.) (3) Find the probability that during a given month there are no near misses on landings and lakeuffs at the airpcrt. : (b) Find the probability that during a given month there are Four near misses S (c) Find the probability that there are at least four near misses during a particuiar month : The number x of people entering the intensive care unit at a particular hospital on anyr one clay has a Poisson probability distribution with mean equal to ve persons per day. (a) What is the probability that the number of people entering the intensive care unit on a particular dayr is two? (Round your answer to three decimal places.) |:| What is the probability that the number of people entering the intensive care unit on a particular day is less than or equal to two? (Round your answer to three decimal places.) |:| (b) Is it likely that xwill exceed 16? Explain. 0 Yes, x is less than 2 standard deviations above the mean. 0 No, x is more than 2 standard deviations above the mean. According to a study conducted by a university, children who are injured three Or more times tend to sustain these injuries during a relatively limited time, usually 1 year or less. If the average number of injuries peryear for schoolrage children is three, what are the prebabilities of these events? (Reund yuur answers tu three decimal places) (a) a schoolrage child will sustain three injuries during the year : (b) a schoolrage child will sustain three or more injuries during the year E (c) a schoolrage child will sustain at must ene injury during the year :