05 Normal Distribution

# 05 Normal Distribution - The Normal Distribution Also Known...

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The Normal Distribution Also Known As The Gaussian Distribution D&B 4.1,4.3,4.6*

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But first a recap: z Observation z Analysis z Understanding z Judgment z Action
100 people each flipping 100 coins z Observation z Analysis z Understanding z Judgment z Action 35 40 45 50 55 60 65 01 0 2 3 x

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HHTTT,HTHTT,HTTHT,HTTTH, etc. z Observation z Analysis z Understanding z Judgment z Action z We can represent what we observe by enumerating all the possible combinations of events and determining the probability of each event occurring.
Model: A simplified representation of our understanding z Observation z Analysis z Understanding z Judgment z Action x n x p p x n p n x P = ) 1 ( ) , | ( z We can create a model that represents simply all the possible outcomes and the respective probabilities.

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We can use that understanding, those models, to make predictions z Observation z Analysis z Understanding z Judgment z Action z Simulate the process { X~B( n,p ) z rbinom z Determine probabilities { P(X=x| n,p ) z dbinom { P(X<x| n,p ) z pbinom z Extract quantiles { X(P<p| n,p ) z qbinom
What are the chances of that happening? z Observation z Analysis z Understanding z Judgment z Action z Eighty percent of the turtle hatchlings on an island are female. Could this have occurred by chance or can this be used as evidence of the population reacting to environmental stress?

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What are the chances of that happening? z Observation z Analysis z Understanding z Judgment z Action z Sea turtles have temp. dependent sex determination. z Often populations have a 50-50 ratio of males- females. z Having 80% females is not likely (we could test this).
What action should be taken? z Observation z Analysis z Understanding z Judgment z Action z Enumerating the possibilities.

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05 Normal Distribution - The Normal Distribution Also Known...

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