The Normal Distribution

May 28, 2012

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The Normal Distribution

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The Normal Distribution

The Normal Distribution. Notes and review problems. The Normal Distribution. A normal variable is continuous, ranges from – ¥ to + ¥ , and forms a symmetrical distribution, with a mean m and a standard deviation s. m. f(x). f(x). The Normal Distribution. The density function f(x) is .

1.1k views • 21 slides

The Normal Distribution

The Normal Distribution. Today, we will revisit the Empirical Rule and other characteristics of the normal distribution. The Empirical Rule. The Empirical Rule: 68% of the data under a normal curve lies within one standard deviation of the mean.

500 views • 17 slides

The normal distribution

The normal distribution. Binomial distribution is discrete events, (infected, not infected) The normal distribution is a probability density function for a continuous variable, and is represented by a continuous curve. Density = relative frequency of varites on the Y (horizontal) axis.

488 views • 26 slides

The Normal Distribution

The Normal Distribution. The Normal Distribution. Distribution – any collection of scores, from either a sample or population Can be displayed in any form, but is usually represented as a histogram

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The Normal Distribution

The Normal Distribution. BUSA 2100, Sections 3.3, 6.2. Introduction to the Normal Distribution. The normal distribution is the most widely used probability distribution. Reason : Most variables observed in nature and many variables in business are “normally distributed.”

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The Normal Distribution

The Normal Distribution. AMIN SOKHANVAR 2013-12-27. Airline Passenger Loading Times.

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The Normal Distribution

The Normal Distribution . Lesson 2 . Starter: Find P ( Z<1.63). To do this we begin with a sketch of the normal distribution. We then mark a line to represent Z=1.63 P(Z<1.63) is the area under the curve to the left of a. We now use the table to look up this probability

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The Normal Distribution

The Normal Distribution. Chapter 6. 6-1 Introduction 6-2 Properties of a Normal Distribution 6-3 The Standard Normal Distribution 6-4 Applications of the Normal Distribution 6-5 The Central Limit Theorem 6-7 Summary. Outline. Objectives:

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The Normal Distribution

The Normal Distribution. Many thanks to the authors of IB Mathematical Studies Standard Level: For the IB diploma (International Baccalaureate) by Peter Blythe, Jim Fensom , Jane Forrest and Paula Waldman De Tokman (26 Jul 2012).

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The Normal Distribution

Chapter 9 Probability Distributions. 9.3. The Normal Distribution. MATHPOWER TM 12, WESTERN EDITION. 9.3. 1. Normal Distribution. Many sets of data have common characteristics in how they are distributed. One of the most important probability distributions is the normal distribution.

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The Normal Distribution

The Normal Distribution. (A) Random Variables. Now we wish to combine some basic statistics with some basic probability  we are interested in the numbers that are associated with situations resulting from elements of chance i.e. in the values of random variables

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The Normal Distribution

The Normal Distribution. Prepared by E.G. Gascon. Properties of Normal Distribution. Peak. Image text page 487. It’s peak occurs directly above the mean The curve is symmetric about the vertical line through the mean. The curve never touches the x-axis

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The Normal Distribution…

The Normal Distribution…. An important function that can’t be integrated (by elementary methods) and why we need numerical methods!. The Normal Distribution…. Z-values are used to calculate probabilities or estimate the fraction of a statistic that lies within a given range.

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The Normal Distribution

The Normal Distribution. The average (mean) IQ in America is 100 with a standard deviation of 15. Assume that IQs are normally distributed. a. Find the percentage of people with IQ lower than 69.

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The Normal Distribution

The Normal Distribution. Using Models to Describe Data Distributions. The Density Curve All density curves are based on mathematical models (“equations”) that can be used to describe the frequency for a given datum The area under all densities curves equals 1. the model. the data.

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The Normal Distribution

The Normal Distribution. The Area under the curve. The area under the curve represents everything: 100%. The mean is in the middle. 50% of the data is below the mean. 50% of the data is above the mean. Remember that the mean=median=mode!. Within one standard deviation. P(-1<Z<1) = 68%.

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The Normal Distribution & Standard Normal Distribution

The Normal Distribution & Standard Normal Distribution. I The Normal Distribution A What is it? B Why is it everywhere? Probability Theory is why C The Skewed Normal Distribution D Kurtosis II The Standard Normal Distribution A Standardizing a Normal Distribution

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The Normal Distribution

The Normal Distribution. Lake Maggiore, St. Petersburg, Florida. Alligators are only native to the United States and China. The mean length of an American adult male is 11.2 feet with a standard deviation of 2.06 feet and an approximately normal distribution.

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The Normal distribution

The Normal distribution. and the 68-95-99.7 Rule. skewed distributions & outliers. Normal = typical. This is valuable information when studying human behavior

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The Normal Distribution

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The Normal Distribution

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The Normal Distribution

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Presentation Transcript

The Normal Distribution

The Normal Distribution

The normal distribution

The Normal Distribution

The Normal Distribution

The Normal Distribution

The Normal Distribution

The Normal Distribution

The Normal Distribution

The Normal Distribution

The Normal Distribution

The Normal Distribution

The Normal Distribution…

The Normal Distribution

The Normal Distribution

The Normal Distribution

The Normal Distribution &amp; Standard Normal Distribution

The Normal Distribution

The Normal distribution

The Normal Distribution

The Normal Distribution

The Normal Distribution & Standard Normal Distribution