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S TATISTICS. E LEMENTARY. Chapter 5 Normal Probability Distributions. M ARIO F . T RIOLA. E IGHTH. E DITION. Continuous random variable Normal distribution. Overview. 5-1. Continuous random variable Normal distribution. Curve is bell shaped and symmetric. µ Score. - PowerPoint PPT Presentation

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4-5 The Poisson Distribution

MARIO F. TRIOLAEIGHTHEDITIONELEMENTARYSTATISTICSChapter 5 Normal Probability Distributions#Chapter 5. Section 5-1 and 5-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Continuous random variable Normal distributionOverview5-1#Chapter 5. Section 5-1 and 5-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longmanpage 226 of textThis is the first time the symmetric bell-shaped curve has been called a normal distribution. Continuous random variable Normal distributionCurve is bell shapedand symmetricScoreOverview5-1Figure 5-1#Chapter 5. Section 5-1 and 5-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Continuous random variable Normal distributionCurve is bell shapedand symmetricScoreFormula 5-1Overview5-1Figure 5-1x - 2y =12e 2 p( )#Chapter 5. Section 5-1 and 5-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley LongmanEven though the equation appears daunting, with the knowledge of and , it is the same as any other equation relating x and y. Remind student that e and are constant values.The result is bell shape curve. With a graphing calculator, the instructor can show the graph of the equation with = 0 and = 1. 5-2

The Standard Normal Distribution#Chapter 5. Section 5-1 and 5-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Uniform Distribution a probability distribution in which the continuous random variable values are spread evenly over the range of possibilities; the graph results in a rectangular shape.Definitions#Chapter 5. Section 5-1 and 5-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longmanpage 227 of text Density Curve (or probability density function) the graph of a continuous probability distribution Definitions#Chapter 5. Section 5-1 and 5-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley LongmanRemind students that the area of a probability density curve must equal 1 as the total of all probabilities of a probability distribution equals 1. Density Curve (or probability density function) :The graph of a continuous probability distribution Definitions1. The total area under the curve must equal 1.

2. Every point on the curve must have a vertical height that is 0 or greater.

#Chapter 5. Section 5-1 and 5-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley LongmanRemind students that the area of a probability density curve must equal 1 as the total of all probabilities of a probability distribution equals 1. Because the total area under the density curve is equal to 1, there is a correspondence between area and probability.#Chapter 5. Section 5-1 and 5-2. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longmanpage 228 of textThis is an important fact for students to understand.