Basic Business Statistics,9th Edition基本業(yè)務(wù)統(tǒng)計第九版

1、Basic Business Statistics (9th Edition)Chapter 6The Normal Distribution and Other Continuous Distributions1Chapter TopicsThe Normal DistributionThe Standardized Normal DistributionEvaluating the Normality AssumptionThe Uniform DistributionThe Exponential Distribution2Continuous Probability Distribut

2、ionsContinuous Random VariableValues from interval of numbersAbsence of gapsContinuous Probability DistributionDistribution of continuous random variableMost Important Continuous Probability DistributionThe normal distribution3The Normal Distribution“Bell ShapedSymmetricalMean, Median and Mode are E

3、qualInterquartile RangeEquals 1.33 sRandom VariableHas Infinite RangeMean Median ModeXf(X)4The Mathematical Model5Many Normal DistributionsVarying the Parameters and , We Obtain Different Normal DistributionsThere are an Infinite Number of Normal Distributions6The Standardized Normal DistributionWhe

4、n X is normally distributed with a mean and a standard deviation , follows a standardized (normalized) normal distribution with a mean 0 and a standard deviation 1.Xf(X)f(Z)7Finding ProbabilitiesProbability is the area under the curve!cdXf(X)8Which Table to Use?Infinitely Many Normal Distributions M

5、eans Infinitely Many Tables to Look Up!9Solution: The Cumulative Standardized Normal DistributionZ.00.010.0.5000.5040.5080.5398.54380.2.5793.5832.58710.3.6179.6217.6255.5478.020.1.5478Cumulative Standardized Normal Distribution Table (Portion) ProbabilitiesOnly One Table is NeededZ = 0.1210Standardi

6、zing ExampleNormal DistributionStandardized Normal Distribution11Example:Normal DistributionStandardized Normal Distribution12Z.00.010.0.5000.5040.5080.5398.54380.2.5793.5832.58710.3.6179.6217.6255.5832.020.1.5478Cumulative Standardized Normal Distribution Table (Portion) Z = 0.21Example:(continued)

7、13Z.00.01-0.3.3821.3783.3745.4207.4168-0.1.4602.4562.45220.0.5000.4960.4920.4168.02-0.2.4129Cumulative Standardized Normal Distribution Table (Portion) Z = -0.21Example:(continued)14Normal Distribution in PHStatPHStat | Probability & Prob. Distributions | Normal Example in Excel Spreadsheet15Example

8、:Normal DistributionStandardized Normal Distribution16Example:(continued)Z.00.010.0.5000.5040.5080.5398.54380.2.5793.5832.58710.3.6179.6217.6255.6179.020.1.5478Cumulative Standardized Normal Distribution Table (Portion) Z = 0.3017.6217Finding Z Values for Known ProbabilitiesZ.000.20.0.5000.5040.5080

9、0.1.5398.5438.54780.2.5793.5832.5871.6179.6255.010.3Cumulative Standardized Normal Distribution Table (Portion)What is Z Given Probability = 0.6217 ?.621718Recovering X Values for Known ProbabilitiesNormal DistributionStandardized Normal Distribution19More Examples of Normal Distribution Using PHSta

10、tA set of final exam grades was found to be normally distributed with a mean of 73 and a standard deviation of 8.What is the probability of getting a grade no higher than 91 on this exam?2.259120What percentage of students scored between 65 and 89?28965-1More Examples of Normal Distribution Using PH

11、Stat(continued)21Only 5% of the students taking the test scored higher than what grade?1.645? =86.16(continued)More Examples of Normal Distribution Using PHStat22The middle 50% of the students scored between what two scores?0.6778.467.6-0.67.25.25More Examples of Normal Distribution Using PHStat(con

12、tinued)23Assessing NormalityNot All Continuous Random Variables are Normally DistributedIt is Important to Evaluate How Well the Data Set Seems to Be Adequately Approximated by a Normal Distribution24Assessing NormalityConstruct ChartsFor small- or moderate-sized data sets, do the stem-and-leaf disp

13、lay and box-and-whisker plot look symmetric?For large data sets, does the histogram or polygon appear bell-shaped?Compute Descriptive Summary MeasuresDo the mean, median and mode have similar values?Is the interquartile range approximately 1.33 s?Is the range approximately 6 s?(continued)25Assessing

14、 NormalityObserve the Distribution of the Data SetDo approximately 2/3 of the observations lie between mean 1 standard deviation?Do approximately 4/5 of the observations lie between mean 1.28 standard deviations?Do approximately 19/20 of the observations lie between mean 2 standard deviations?Evalua

15、te Normal Probability PlotDo the points lie on or close to a straight line with positive slope?(continued)26Assessing NormalityNormal Probability PlotArrange Data into Ordered ArrayFind Corresponding Standardized Normal Quantile ValuesPlot the Pairs of Points with Observed Data Values on the Vertica

16、l Axis and the Standardized Normal Quantile Values on the Horizontal AxisEvaluate the Plot for Evidence of Linearity(continued)27Assessing NormalityNormal Probability Plot for Normal DistributionLook for Straight Line!306090-2-1012ZX(continued)28Normal Probability PlotLeft-SkewedRight-SkewedRectangu

17、larU-Shaped306090-2-1012ZX306090-2-1012ZX306090-2-1012ZX306090-2-1012ZX29Obtaining Normal ProbabilityPlot in PHStatPHStat | Probability & Prob. Distributions | Normal Probability PlotEnter the range of the cells that contain the data in the Variable Cell Range window30The Uniform DistributionPropert

18、ies:The probability of occurrence of a value is equally likely to occur anywhere in the range between the smallest value a and the largest value bAlso called the rectangular distribution 31The Uniform DistributionThe Probability Density FunctionApplication: Selection of random numbersE.g., A wooden

19、wheel is spun on a horizontal surface and allowed to come to rest. What is the probability that a mark on the wheel will point to somewhere between the North and the East?(continued)32Exponential DistributionsE.g., Drivers arriving at a toll bridge; customers arriving at an ATM machine33Exponential Distributions