NORMAL1 - 4.3 NORMAL PROBABILITY DISTRIBUTIONS The Most...

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Unformatted text preview: 4.3 NORMAL PROBABILITY DISTRIBUTIONS The Most Important Probability Distribution in Statistics A random variable X with mean and standard deviation is normally distributed if its probability density function is given by ... 71828 . 2 e and ... 14159 . 3 where x e 2 1 ) x ( f 2 x ) 2 / 1 ( = = - = -- Normal Distribution The Shape of the Normal Distribution The normal distribution is bell shaped, and symmetrical around . y symmetrical? Let = 100. Suppose x = 110. 2 2 10 ) 2 / 1 ( 100 110 ) 2 / 1 ( e 2 1 e 2 1 ) 110 ( f - -- = = Now suppose x = 90 2 2 10 ) 2 / 1 ( 100 90 ) 2 / 1 ( e 2 1 e 2 1 ) 90 ( f -- -- = = 110 90 Normal Probability Distributions The expected value (also called the mean ) can be any number The standard deviation can be any nonnegative number There are infinitely many normal distributions The effects of The effects of and and How does the standard deviation affect the shape of f(x)? = 2 =3 =4 = 10 = 11 = 12 How does the expected value affect the location of f(x)? X 8 3 6 9 12 A family of bell-shaped curves that differ only in their means and standard deviations. = the mean of the distribution = the standard deviation = 3 and = 1 X 3 6 9 12 X 3 6 9 12 = 3 and = 1 = 6 and = 1 X 8 3 6 9 12 X 8 3 6 9 12 = 6 and = 2 = 6 and = 1 X...
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NORMAL1 - 4.3 NORMAL PROBABILITY DISTRIBUTIONS The Most...

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