Transcription of Examples of Continuous Probability Distributions
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Example: air traffic controller
Examples of Continuous Probability Distributions
Examples of Continuous Probability Distributions :The normal and standard normalThe normal DistributionXf(X)Changing shifts the distribution left or increases or decreases the normal Distribution:as mathematical function (pdf)2)(2121)( =xexfNote constants: = is a bell shaped curve with different centers and spreads depending on and The normal PDFIt s a Probability function, so no matter what the values of and , must integrate to 1!1212)(21= + dxex normal distribution is defined by its mean and standard dev. E(X)= = Var(X)= 2 =Standard Deviation(X)= dxexx + 2)(2121 2)(212)21(2 + dxexx**The beauty of the normal curve: No matter what and are, the area between - and + is about 68%; the area between -2 and +2 is about 95%; and the area between -3 and +3 is about Almost all values fall within 3 standard deviations.
The Normal Probability Plot • Normal probability plot – Order the data. – Find corresponding standardized normal quantile values: – Plot the observed data values against normal quantile values. – Evaluate the plot for evidence of linearity. that correspond s to a particular left -tail area
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