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stat 20 chap5

# stat 20 chap5 - Stat 20 Chap 5 Normal curve Why do we study...

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Stat 20 Chap 5. Normal curve Why do we study normal distribution? Many real data approximately follow normal distribution It has many nice properties What is a normal distribution? N ( μ, σ 2 ) = 1 2 πσ exp( - ( x - μ ) 2 σ 2 ) μ is mean and σ is standard deviation Each pair of μ and σ defines a normal distribution When μ = 0 and σ = 1, it is called standard normal distri- bution Characteristics of the standard normal distribution (i.e. nor- mal curve) Symmetric about 0 Bell shape Total area = 100% – recall histogram Other names: Gaussian curve, bell curve 1

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Properties of standard normal curve The area under the normal curve between -1 and 1 is about 68% The area under the normal curve between -2 and 2 is about 95% The area under the normal curve between -3 and 3 is about 99 . 7% Other area can be found using tables (page A104 in textbook) 2
Examples: 1. Find the area between 0 and 1 under the normal curve 2. Find the area to the right of 1 under the normal curve 3. Find the area between -1 and -2 under the normal curve

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stat 20 chap5 - Stat 20 Chap 5 Normal curve Why do we study...

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