Lec07

# Lec07 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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© 2008 Haipeng Shen 1/31/08 Lecture 7 1 STOR 155 Introductory Statistics Lecture 7: The Normal Distributions (II) The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

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© 2008 Haipeng Shen 1/31/08 Lecture 7 2 Review Density curves Normal distributions and normal curves The standard normal distribution The 68-95-99.7 rule for normal distributions Standardizing observations
© 2008 Haipeng Shen 1/31/08 Lecture 7 3 Topics The standard normal table Normal distribution calculation Normal quantile plot

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© 2008 Haipeng Shen 1/31/08 Lecture 7 4 The standard normal distribution The standard normal distribution is the normal dist. with mean 0 and standard deviation 1 , denoted as N(0,1) . N(0,1) can be treated as a baseline. Any normal distribution can be related to N(0,1) by a linear transformation. Z: N(0,1) , what is the distribution for X=a+bZ ?
© 2008 Haipeng Shen 1/31/08 Lecture 7 5 Table A: The Standard Normal Table Table A is a table of areas under the standard normal density curve. The table entry for each value z is the area under the curve to the left of z .

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© 2008 Haipeng Shen 1/31/08 Lecture 7 6 Table A : The Standard Normal Table Table A can be used to find the proportion of observations of a variable which fall to the left of a specific value z if the variable follows a normal distribution.
© 2008 Haipeng Shen 1/31/08 Lecture 7 7

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© 2008 Haipeng Shen 1/31/08 Lecture 7 8 Example If Z has a standard normal distribution, determine the value z for which the area under the normal curve between 0 and z is 0.4192. z =1.4 or -1.4
1/31/08 Lecture 7 9 Example z A is defined as the z value for which the area to the right of z A under the standard normal curve is A . Determine z 0.0808 . 1.4

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Lec07 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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