Lecture 8_normal distribution

# Lecture 8_normal distribution - The Normal Distribution 1...

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9/20/2010 1 The Normal Distribution 1 Probability Distributions • The basis of our inferences from samples to populations are probability distributions – Probability distributions are integral equations that generate curves when they are plotted – Think of the distributions as smoothed out versions of histograms from a continuous variable that has been sampled repeatedly over an infinite number of observations 2 The Normal Distribution • The most commonly used probability distribution in statistics is the unit normal distribution , formed from z-scores – The unit normal distribution is also known as the “normal curve” or the “bell curve” or the “Gaussian curve” 3

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9/20/2010 2 Carl Gauss 4 “Gauss was a prodigious mental calculator. Reputedly, when asked how he had been able to predict the trajectory of [the dwarf planet] Ceres with such accuracy he replied, „I used logarithms.‟ The questioner then wanted to know how he had been able to look up so many numbers from the tables so quickly. „Look them up?‟ Gauss responded. „Who needs to look them up? I just calculate them in my head!‟” More on the Normal Distribution • It is not a single curve; it is an infinite number of possible curves represented by a common equation • Thus there are a “family” of normal curves, each defined by unique mean and variance parameters 5 More on the Normal Distribution • The normal distribution is symmetrical – Most scores are clustered in the middle, with
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Lecture 8_normal distribution - The Normal Distribution 1...

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