Homework ReviewModelsArea And ProbabilityDensity FunctionsThe Normal DistributionExamplesAssignmentAnswers to Even-numbered ExercisesModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesModeling Continuous VariablesLecture 19Sections 6.1 - 6.3.1Robb T. KoetherHampden-Sydney CollegeTue, Sep 29, 2009ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesOutline1Homework Review2Models3Area And ProbabilityDensity Functions4The Normal DistributionExamples5Assignment6Answers to Even-numbered ExercisesModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesOutline1Homework Review2Models3Area And ProbabilityDensity Functions4The Normal DistributionExamples5Assignment6Answers to Even-numbered ExercisesModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesHomework ReviewExercise 5.20, page 336.Consider the following two frequency plots based on twosets of data with 10 observations:-2 210-1Frequency Plot 1-2 210-1Frequency Plot 2Note that Plot 1 can be converted to Plot 2 by moving thetwo blue X’s.ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesHomework ReviewExercise 5.20, page 336.(a) Do you think the range for Plot 1 is smaller than, equalto, or larger than the range for Plot 2?(b) Do you think the mean for Plot 1 is smaller than, equalto, or larger than the mean for Plot 2?(c) Do you think the standard deviation for Plot 1 is smallerthan, equal to, or larger than the standard deviation forPlot 2? Explain.(d) Check your answers to parts (a), (b), and (c) bycomputing the range, mean, and standard deviation foreach set of data.ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesHomework ReviewSolution(a) The ranges are clearly equal.(b) Both distributions are symmetric, so the means are inthe center, at 0. Thus, they are equal.(c) The two blue points in Plot 2 are closer to the mean thanthey are in Plot 1, so they have smaller deviations. Allother points are the same between the two distributions.Thus, Plot 2 has a smaller standard deviation.ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesHomework ReviewSolution(d) For Plot 1,range = 2 − (−2) = 4.x =010= 0.SSX = 4 + 4 + 1 + 1 + 0 + 0 + 1 + 1 + 4 + 4= 20.s =r209= 1.491.ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesHomework ReviewSolution(d) For Plot 2,range = 2 − (−2) = 4.x =010= 0.SSX = 4 + 1 + 1 + 0 + 0 + 0 + 0 + 1 + 1 + 4= 12.s =r129= 1.155.ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesOutline1Homework Review2Models3Area And ProbabilityDensity Functions4The Normal DistributionExamples5Assignment6Answers to Even-numbered ExercisesModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesModelsDefinition (Mathematical model)A mathematical model is a mathematical abstraction and,therefore, a simplification of a real situation, one that retainsthe essential features.Real situations are usually much too complicated todeal with in all their details.ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesExampleThe “bell curve” is a model (an abstraction) of manypopulations.Real populations have all sorts of bumps and twists andirregularities.The bell curve is smooth and perfectly symmetric.In statistics, the bell curve is called the normal curve, ornormal distribution.ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesModelsOur models will be models of distributions, presentedeither as histograms or as continuous distributions.ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesOutline1Homework Review2Models3Area And ProbabilityDensity Functions4The Normal DistributionExamples5Assignment6Answers to Even-numbered ExercisesModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesHistograms and AreaIn a histogram, frequency is represented by area.Consider the following distribution of rainfall data.Rainfall (in) Frequency0.00 - 2.49 92.50 - 4.99 125.00 - 7.49 47.50 - 9.99 210.00 - 12.49 212.50 - 14.99 1ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesHistograms and Area0.0 2.5 10.05.0 7.5 15.012.5630912No. of YearsRainfall (in)ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesHistograms and AreaWhat is the total area of this histogram?ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesHistograms and Area0.0 2.5 10.05.0 7.5 15.012.5630912No. of YearsRainfall (in)3022.551052.5ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea AndProbabilityDensity FunctionsThe NormalDistributionExamplesAssignmentAnswers toEven-numberedExercisesHistograms and AreaThe total area is25 + 30 + 7.5 + 5 + 5 + 2.5 = 75.ModelingContinuousVariablesRobb T.KoetherHomeworkReviewModelsArea
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