Lecture_11,_Chap_7,__Sec_3

Lecture_11,_Chap_7,__Sec_3 - Chapter 7 Section 3...

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Sullivan – Statistics : Informed Decisions Using Data – 2 nd Edition – Chapter 6 Section 2 – Slide 1 of 25 Chapter 7 Section 3 Applications of the Normal Distribution
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Applications of the Normal Distribution Learning objectives Find and interpret the area under a normal curve Find the value of a normal random variable 1 2
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Applications of the Normal Distribution We want to calculate probabilities and values for general normal probability distributions We can relate these problems to calculations for the standard normal in the previous section
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Applications of the Normal Distribution For a general normal random variable X with mean μ and standard deviation σ , the variable has a standard normal probability distribution We can use this relationship to perform calculations for X σ μ - = X Z
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For example, if μ = 3 σ = 2 then a value of x = 4 for X corresponds to a value of z = 0.5 for Z Applications of the Normal Distribution 5 0 2 3 4 . z = - =
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Because of this relationship Values of X  Values of Z then P ( X < x ) = P ( Z < z ) To find P ( X < x ) for a general normal random variable, we could calculate P ( Z < z ) for the standard normal random variable Applications of the Normal Distribution
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Applications of the Normal Distribution This relationship lets us compute all the different types of probabilities Probabilities for X are directly related to probabilities for Z using the ( X μ ) / σ relationship
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Applications of the Normal Distribution A different way to illustrate this relationship a μ b X Z a – μ σ b – μ σ
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Applications of the Normal Distribution σ μ - = x z With this relationship, the following method can be used to compute areas for a general normal random variable X
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This note was uploaded on 04/16/2008 for the course STAT 250 taught by Professor Sims during the Spring '08 term at George Mason.

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Lecture_11,_Chap_7,__Sec_3 - Chapter 7 Section 3...

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