Ch07-Continuous-Probability-Distributions-商务统计学概论(.ppt
CHAPTER 7Continuous Probability Distributionsto accompanyIntroduction to Business Statisticsfourth edition,by Ronald M.WeiersPresentation by Priscilla Chaffe-Stengel Donald N.Stengel 2002 The Wadsworth GroupChapter 7-Learning ObjectivesDifferentiate between the normal and the exponential distributions.Use the standard normal distribution and z-scores to determine probabilities associated with the normal distribution.Use the normal distribution to approximate the binomial distribution.Use the exponential distribution to determine related probabilities.2002 The Wadsworth GroupChapter 7-Key TermsProbability density functionProbability distributionsStandard normal distributionMean,variance,applicationsExponential distributionMean,variance,applicationsNormal approximation to the binomial distribution 2002 The Wadsworth GroupChapter 7-Key ConceptThe area under a probability density function between two bounds,a and b,is the probability that a value will occur within the bounded interval between a and b.2002 The Wadsworth GroupAreas under the Normal CurveUse the standard normal table to find:The z-score such that the area from the midpoint to z is 0.20.In the interior of the standard normal table,look up a value close to 0.20.The closest value is 0.1985,which occurs at z=0.52.2002 The Wadsworth GroupAreas under the Normal CurveUse the standard normal table to find:The probability associated with z:P(0 z 1.32).Locate the row whose header is 1.3.Proceed along that row to the column whose header is.02.There you find the value.4066,which is the amount of area capture between the mean and a z of 1.32.Answer:0.4066 2002 The Wadsworth GroupAreas under the Normal CurveUse the standard normal table to find:The probability associated with z:P(1.10 z 1.32).Find the amount of area between the mean and z=1.32 and add it to the amount of area between the mean and z=1.10*.0.3643+0.4066=0.7709 2002 The Wadsworth GroupAreas under the Normal CurveUse the standard normal table to find:The probability associated with z:P(1.00 z 1.32).Find the amount of area between the mean and z=1.00 and subtract it from the amount of area between the mean and z=1.32.0.4066 0.3413=0.0653 2002 The Wadsworth GroupStandardizing Individual Data Values on a Normal CurveThe standardized z-score is how far above or below the individual value is compared to the population mean in units of standard deviation.“How far above or below”=data value mean“In units of standard deviation”=divide by sStandardized individual value 2002 The Wadsworth GroupAn Example,cont.Given in the problem:=12.1 minutes,s=2.0 minutesa)Greater than 14.1 minutesP(x 14.1)=P(z 1.00)=.5 .3413=0.1587z=xms=14.112.12.0=1.00 2002 The Wadsworth GroupAn Example,cont.Given in the problem:=12.1 minutes,s=2.0 minutesc)Between 10.1 and 14.1 minutesP(10.1 x 14.1)=P(1.00 z 1.00)=0.3413+0.3413=0.6826zlower=xms=10.112.12.0=1.00zupper=xms=14.112.12.0=1.00 2002 The Wadsworth GroupAn Example,cont.Given in the problem:=12.1 minutes,s=2.0 minutesd)Between 10.1 and 16.1 minutesP(10.1 x 16.1)=P(1.00 z 2.00)=0.3413+0.4772=0.8185 2002 The Wadsworth GroupExample:Using Microsoft ExcelProblem:What is the probability that the time required for Mary and her bags to get to the room will be:c)between 10.1 and 14.1 minutes?In a cell on an Excel worksheet,type all on one line=NORMDIST(14.1,12.1,2,true)-NORMDIST(10.1,12.1,2,true)and you will see the answer:0.6826d)between 10.1 and 16.1 minutes?In a cell on an Excel worksheet,type all on one line=NORMDIST(16.1,12.1,2,true)-NORMDIST(10.1,12.1,2,true)and you will see the answer:0.8185 2002 The Wadsworth GroupThe Exponential Distribution where l=mean and standard deviation e=2.71828,a constantProbability:Application:Every day,drivers arrive at a tollbooth.If the Poisson distribution were applied to this process,what would be an appropriate random variable?What would be the exponential distribution counterpart to this random variable?2002 The Wadsworth Group
