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# hw4.pdf - CH 6 Continuous Probability Distribution–Normal...

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CH 6: Continuous Probability Distribution–Normal Distribution 1. Characteristics of a Normal Distribution: (A) The distribution is bell-shaped with mean μ and standard deviation σ . (B) The total area under the curve is 1. (C) The empirical rule holds. (D) The distribution function: f ( x ) = 1 σ p 2 e ( x - μ ) 2 2 σ 2 for -1 < x < 1 (E) The probability of observing the value x between a and b : P ( a x b ) = Area under the curve between a and b (F) Notation N ( μ, σ ) 2. Standard Normal Distribution (A) The standard normal distribution had a bell-shaped distribution with mean μ = 0 and standard deviation σ = 1. It is denoted by N (0 , 1), and the random variable is denoted by Z (instead of X ). (B) We use the z -table to find the probability (area under the curve). (C) The z -table represents the area under the curve to the left of a given value (left-tail). Case 1 (left-tail): To find the probability P ( Z a ), we use the table directly. EX 1 Draw the graph of standard normal and use the z-table to find P ( z 1 . 10) =
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