The Normal Curve Notes 9-27-17.docx

# The Normal Curve Notes 9-27-17.docx - CIS 343 Notes Bell...

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CIS 343 Notes 9-27-17 Bell Curve Two things are happening in the excel file: 1. The Weak Law of Large Numbers: As n gets bigger, the probability of Xbar is moving toward the middle, toward the true value. (of observations) 2. The Central Limit Theorem: As n goes up, the shape of the probabilities of Xbar are more and more normal Let x = 1 measurement Then x tends to be around mu, but it is not unusual to be off by σ in either direction The above is true for every measurement Let Xbar be the average of n measurements Then Xbar tends to be around mu ( μ) , but it is not unusual to be off by σ/sqrt(n) in either direction Mu + 3 σ Mu - 2 σ Mu- σ Mu Mu + σ Mu + 2 σ Mu+3 σ Typical data point is this far from MU

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