What is the probability that exactly three people will arrive at the bank during a 2- minute period on Monday mornings to make a deposit or a withdrawal? What is the probability that five or more customers will arrive during an 8- minute period?

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Mean and Standard Deviation of a Poisson distributionThe mean or expected value of a Poisson’s Distribution is . It is the long run average of occurrences for an interval if many random samples are taken. This gives the actual occurrences that are likely to happen.The variance of a Poisson distribution is also . The standard deviation is . Poisson Distribution as an approximation of the Binomial distributionCertain types of binomial distribution problems can be approximated by using the Poisson’s distribution. Binomial problem with large sample sizes and small values of p, which then generate rare events, are potential candidate for use of the Poisson distribution. As a rule of thumb, if n>20 and, the approximation is close enough to use the Poisson’s distribution for binomial problems. Poisson Probability Distribution is an approximation of the Binomial!)()(xenpxPnpx7.pn

Exercise.5.24A medical researcher estimates that .00004 of the population has a rare blood disorder. If the researcher randomly selects 100,000 people form the population, what is the probability that seven or more people will have the rare blood disorder?What is the probability that more than 10 people will have the rare blood disorder? Suppose that the researcher gets more than 10 people who have the rare blood disorder in the sample of 100,000 but the sample was taken form a particular geographic region. What might the researcher conclude from the results?

5.21. The average number of annual trips per family to amusement parks in the United States is Poisson Distributed, with a mean of 0.6 trips per year. What is the probability of randomly selecting an American family and finding the following:a.The family did not make a trip to an amusement park last year?b.The family took exactly one trip to an amusement park last year?c.The family took two or more trips to amusement parks last year?d.The family took three or fewer trips to amusement parks over three year period?e.The family took exactly four trips to amusement parks during a six year period?a