Chapter 7: The Normal Distribution

Beschreibung

describing population distributions; normal distributions
Erin Vales
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Erin Vales
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Zusammenfassung der Ressource

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The Normal Curve A bell shaped density curve centered at its mean (mu).
Normal Distribution
Aspects of a Normal Distribution
Importance of Normal Distribution 1. Used to determine the probability that a measurement of a normal random variable falls in a particular interval 2. Used to determine the area under the curve in a certain interval or the proportion (or percentage) of the measurements that fall in a certain interval 3. Used to determine the value of the normal random variable X to guarantee a given probability or percentage
Notation of Normal Distribution
Empirical Rule / 68-95-99.7 Rule
Standard Normal Distribution (Z) Z~N(0,1) Total Area under standard normal curve = 1 It's probabilities (or proportions or percentages) are tabled
Z Table To use standard normal table to find probabilities... - read the value of z down the left most column - then read across the top row - then find the probability in the body of the table **Z table can only be used to find probabilities less than or equal to the value of z specified
Z- score To find the greater than area under the standard normal curve.... P(Z > z) = 1 - P(Z < z) To find the probability that Z falls between a and b .... P(a < Z < b)
Z-score transformations Z = (value - mean)/standard deviation
Probability of X in an Interval
Z Score Transformation Example (1)
Z Score Transformation Example (2)
Z Score Transformation Example (3)
Z Score Transformation Example (4)
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