PPT-The Normal Distribution

Objectives For variables with relatively normal distributions Students should know the approximate percent of observations in a set of data that will fall between the mean and 1 sd 2 sd. Reading: . Chapter 11, Sections 12-1 and 12-2 . of Applied Hydrology. 04/04/2006. 2. Probability. A measure of how likely an event will occur. A number expressing the ratio of favorable outcome to the all possible outcomes . History. Abraham de . Moivre. (1733) – consultant to . gamblers. . Pronunciation. .. Pierre Simon . Laplace – mathematician, astronomer, philosopher, determinist.. Carl Friedrich . Gauss – mathematician and astronomer.. http://www-users.york.ac.uk/~pml1/bayes/cartoons/cartoon08.jpg. 1. Comparison of Named Distributions. discrete. continuous. Bernoulli,. Binomial, Geometric, Negative Binomial, Poisson, Hypergeometric, Discrete Uniform. Distributions. Definition. Many sets of data fit what is called a Normal Distribution: EG.  . Examples when the Normal distribution arises. Looking at the national averages for NCEA.. When measuring heights, weights, arm spans, hand spans . 2.1 Density Curves and the Normal Distributions. 2.2 Standard Normal Calculations. 2. Histogram for Strength of Yarn Bobbins. X. X. X. X. X. X. X. X. X. X. X. X. X. X. X. X. X. X. X. X. X. X. X. X. Bobbin #1: 17.15 g/tex. A Brief Introduction. Normal (Gaussian) Distribution. Bell-shaped distribution with tendency for individuals to clump around the group median/mean. Used to model many biological phenomena. Many . estimators . State:. Express the problem in terms of the observed variable . x. .. Plan:. Draw a picture of the distribution and shade the area of interest under the curve.. Do:. Perform calculations.. Standardize. z. Scores. Chapter 6. The . Bell . Curve is Born (1769). A Modern Normal Curve. Development of a Normal Curve: Sample of 5. Development of a Normal Curve: Sample of 30. Development of a Normal Curve: Sample of 140. 68%-95%-99.7% Rule. Areas under Normal Curve. Areas under Normal Curve(cont). Example: Normal Distribution. The brain weights of adult Swedish males are . approximately. normally distributed with mean μ = 1,400 g and standard deviation . . and Exponential Distributions. 5. Introduction. Several specific distributions commonly occur in a variety of business situations:. N. ormal distribution—a continuous distribution . characterized . La gamme de thé MORPHEE vise toute générations recherchant le sommeil paisible tant désiré et non procuré par tout types de médicaments. Essentiellement composé de feuille de morphine, ce thé vous assurera d’un rétablissement digne d’un voyage sur . Binomial Distribution 1. Binomial Distribution 2. Additional Problems on Binomial Distribution. More Visual Representation. Binomial Distribution Tends to Normal for Large n. Binomial Distribution Tends to Normal for p Close to 0.5. Dehaish. Outlines. Normal distribution. Standard normal distribution . Find probability when known z score . Find z score from known areas . Conversion to Standard normal distribution.. Sampling distribution of sample mean . Normal random variables. The Normal distribution is by far the most important and useful probability distribution in statistics, with many applications in economics, engineering, astronomy, medicine, error and variation analysis, etc. The Normal distribution is often called the bell curve, due to its distinctive shape..