STAT 400 Lecture AL1 Spring 2015 Dalpiaz Examples for 2 6 Poisson Distribution X the number of occurrences of a particular event in an interval of time or space P X x x e x E X Table III pp 580 582 EXCEL x 0 1 2 3 Var X gives P X x POISSON x 0 gives P X x POISSON x 1 gives P X x 1 Traffic accidents at a particular intersection follow Poisson distribution with an average rate of 1 4 per week a What is the probability that the next week is accident free b What is the probability that there will be exactly 3 accidents next week c What is the probability that there will be at most 2 accidents next week d What is the probability that there will be at least 2 accidents during the next two weeks e What is the probability that there will be exactly 5 accidents during the next four weeks f What is the probability that there will be exactly 2 accidents tomorrow g What is the probability that the next accident will not occur for three days h What is the probability that there will be exactly three accident free weeks during the next eight weeks i What is the probability that there will be exactly five accident free days during the next week When n is large n 20 and p is small p 0 05 and n p 5 Binomial probabilities can be approximated by Poisson probabilities For this set 2 n p Suppose the defective rate at a particular factory is 1 Suppose 50 parts were selected from the daily output of parts Let X denote the number of defective parts in the sample a Find the probability that the sample contains exactly 2 defective parts b Use Poisson approximation to find the probability that the sample contains exactly 2 defective parts c Find the probability that the sample contains at most 1 defective part d Use Poisson approximation to find the probability that the sample contains at most 1defective part
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