Chapter 6

# Chapter 6 - Chapter 6 Normal Probability Distributions...

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Chapter 6 Normal Probability Distributions

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Random Variables – single outcome determined by chance Quantitative Continuous Discrete Chapter 5 Chapter 6 Remember:
Chapter 6: Continuous Random Variable a quantitative, continuous variable outcome determined by chance all outcomes independent only 1 outcome at a time Examples: Blood Pressure New same as for Discrete Variables

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Systolic Blood Pressure Systolic Blood Pressure in United States 0 5 10 15 20 25 30 80 90 100 110 120 130 140 150 160 170 180 190 200 Systolic Blood Pressure (mm/Hg) % US Population
Chapter 6 a) Normal Distribution b) Standard Normal Curve c) Finding areas with Standard Normal Curve d) Finding areas with ANY normal curve e) z notation f) Normal Approximation of a binomial distribution

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Probability Distributions for Continuously Random Variables For Real Data , any possible distribution could occur Probability Length
If have lots of observations, can smooth out histogram bars into a probability distribution curve Area under curve still = 1, and reflects relative probabilities of events (density curve) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 x P x ( )

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Example Height of students in this class Expected distribution of heights? Proportion of class 0 0.05 0.10 Height (cm)
Separate by sexes Now separate into 2 groups: predict that men and women have different average height For our class you might expect something closer to: Proportion of class 0 0.05 0.10 Height (cm) women men

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And if you had data for all University students at Maryland Proportion of class 0 0.05 0.10 Height (cm) Women Men Note: with lots of data, Curves tend to smooth out
a) Normal Probability Distributions Often (but by no means always ) continuous random variables have a distribution that is: symmetric bell-shaped This is the Normal Distribution The curve is called a Normal Curve

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Heights of 200 pregnant women Examples of random continuous variables showing approximately normal distribution
Total weight of seeds for one species of sunflower

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http://javaboutique.internet.com/ BallDrop/ With random continuous variables, measurement values tend to fall around the mean So if there is nothing else driving the distribution shape – it will tend towards a normal shape
Random Mechanical Cascade Issue 34 Testing Summer 2009 Games of Chance D. Graham Burnett

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www.princeton.edu/~pear/
If data don’t match normal distribution… Often interested in why not?

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Get a different normal curve for every combination of μ and σ ALL these curves are Normal curves and are symmetric, unimodal, and bell-shaped
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## This document was uploaded on 11/04/2011 for the course BIOM 301 at Maryland.

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Chapter 6 - Chapter 6 Normal Probability Distributions...

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