PPT-6.5 Applications of the Normal Distribution

Objectives By the end of this section I will be able to Compute probabilities for a given value of any normal random variable Find the appropriate value of any normal random variable given an area or probability. Cal State Northridge. . 320. Andrew Ainsworth PhD. The standard deviation. Benefits:. Uses measure of central tendency (i.e. mean). Uses all of the data points. Has a special relationship with the normal curve. 1. 4. Continuous Random Variables and Probability Distributions. 4-1 Continuous Random Variables. 4-2 Probability Distributions and Probability Density Functions. 4-3 Cumulative Distribution Functions. 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 . Harvey Goldstein. Centre for Multilevel Modelling. University of Bristol. The (multilevel) binary . probit. model. . Suppose . that we have a variance components 2-level model for . an . underlying continuous variable written as . History. Abraham de . Moivre. (1733) – consultant to . gamblers. . Pronunciation. .. Pierre Simon . Laplace – mathematician, astronomer, philosopher, determinist.. Carl Friedrich . Gauss – mathematician and astronomer.. 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 . Probability Distribution. Imagine that you rolled a pair of dice. What is the probability of 5-1. ?. To answer such questions, we need to compute the whole population for possible results of rolling two dices. . 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 . @UWE_JT9. @. dave_lush. Scientific . Practice. The Binomial Distribution. This distribution can be seen when the outcomes have discrete values…. eg. rolling dice. Assumptions…. Fixed . number of . 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..