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1、CHAPTER 6Discrete Probability Distributionsto accompanyIntroduction to Business Statisticsfourth edition,by Ronald M.WeiersPresentation by Priscilla Chaffe-Stengel Donald N.Stengel 2002 The Wadsworth GroupChapter 6-Learning ObjectivesDistinguish between discrete and continuous random variables.Diffe
2、rentiate between the binomial and the Poisson discrete probability distributions and their applications.Construct a probability distribution for a discrete random variable,determine its mean and variance,and specify the probability that a discrete random variable will have a given value or value in
3、a given range.2002 The Wadsworth GroupChapter 6-Key TermsRandom variablesDiscrete ContinuousBernoulli processProbability distributionsBinomial distributionPoisson distribution 2002 The Wadsworth GroupDiscrete vs Continuous VariablesDiscrete Variables:Can take on only certain values along an interval
4、the number of sales made in a weekthe volume of milk bought at a storethe number of defective partsContinuous Variables:Can take on any value at any point along an intervalthe depth at which a drilling team strikes oilthe volume of milk produced by a cowthe proportion of defective parts 2002 The Wad
5、sworth GroupThe Bernoulli Process,Characteristics1.There are two or more consecutive trials.2.In each trial,there are just two possible outcomes.3.The trials are statistically independent.4.The probability of success remains constant trial-to-trial.2002 The Wadsworth GroupThe Binomial DistributionTh
6、e binomial probability distribution defines the probability of exactly x successes in n trials of the Bernoulli process.for each value of x.Mean:=E(x)=n pVariance:s2=E(x )2=n p(1 p)2002 The Wadsworth GroupThe Binomial Distribution,An Example Worked by EquationProblem 6.23:A study by the Internationa
7、l Coffee Association found that 52%of the U.S.population aged 10 and over drink coffee.For a randomly selected group of 4 individuals,what is the probability that 3 of them are coffee drinkers?Number Proportion Coffee drinkers(x)3.52 Noncoffee drinkers 1.48Totals 4 1.00So,p=0.52,(1 p)=0.48,x=3,(n x)
8、=1.2002 The Wadsworth GroupThe Binomial Distribution,An Example Worked with TablesProblem:According to a corporate association,50.0%of the population of Vermont were boating participants during the most recent year.For a randomly selected sample of 20 Vermont residents,with x=the number sampled who
9、were boating participants that year,determine:a.E(x)=n p=20 x 0.50=10b.P(x 8)Go to Appendix,Table A.2,n=20.For p=0.5 and k=8,P(x 8)=0.2517c.P(x=10)Go to Appendix,Table A.1,n=20.For p=0.5 and k=10,P(x=10)=0.1762 2002 The Wadsworth GroupExample:Binomial TablesProblem:According to a corporate associati
10、on,50.0%of the population of Vermont were boating participants during the most recent year.For a randomly selected sample of 20 Vermont residents,with x=the number sampled who were boating participants that year,determine:d.P(x=12)Go to Appendix,Table A.1,n=20.For p=0.5 and k=12,P(x=12)=0.1201e.P(7
11、x 13)Go to Appendix,Table A.2,n=20.For p=0.5 and k=13,P(x 13)=0.9423 For p=0.5 and k=6,P(x 6)=0.0577 P(7 x 13)=0.9423 0.0577=0.8846 2002 The Wadsworth GroupExample:Using Microsoft ExcelProblem:According to a corporate association,50.0%of the population of Vermont were boating participants during the
12、 most recent year.For a randomly selected sample of 20 Vermont residents,with x=the number sampled who were boating participants that year,determine:d.P(x=12)In a cell on an Excel worksheet,type=BINOMDIST(12,20,0.5,false)and you will see the answer:=0.1201e.P(7 x 13)In a cell on an Excel worksheet,t
13、ype=BINOMDIST(13,20,0.5,true)-BINOMDIST(6,20,0.5,true)and you will see the answer:=0.8846 2002 The Wadsworth GroupThe Poisson Distribution,Working with the EquationExample,Problem 6.36:During the 12 p.m.1 p.m.noon hour,arrivals at a curbside banking machine have been found to be Poisson distributed
14、with a mean of 1.3 persons per minute.If x=number of arrivals per minute,determine:b.c.d.P(x 2)=0.8571 from Appendix Table A.4,l=1.3,k=2 2002 The Wadsworth GroupThe Poisson Distribution,Using Microsoft ExcelExample,Problem 6.36:b.P(x=0)In a cell in an Excel spreadsheet,type=POISSON(0,1.3,false)and you will see the answer:=0.2725c.P(x=1)In a cell in an Excel spreadsheet,type=POISSON(1,1.3,false)and you will see the answer:=0.3543d.P(x 2)In a cell in an Excel spreadsheet,type=POISSON(2,1.3,true)and you will see the answer:=0.8571 2002 The Wadsworth Group