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. 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. 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. Normal distribution. Lognormal distribution. Mean, median and mode. Tails. Extreme value distributions. Normal (Gaussian) distribution. P. robability density function (PDF). What does figure tell about the cumulative distribution function . The Normal Curve, Skewness, Kurtosis, and Probability. VON CHRISTOPHER G. CHUA, LPT, MST. Affiliate, ESSU-Graduate School. MAED 602: STATISTICAL METHODS. Session Objectives. In this fraction of the course on Statistical Methods, graduate students enrolled in the subject are expected to do the following:. 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. 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 . Section 2.2. Normal Distributions. After this section, you should be able to…. DESCRIBE and APPLY the 68-95-99.7 Rule. DESCRIBE the standard Normal Distribution. PERFORM Normal distribution calculations. Copyright © Cengage Learning. All rights reserved. 5 Joint Probability Distributions and Random Samples Copyright © Cengage Learning. All rights reserved. 5.4 The Distribution of the Sample Mean It is also known as the Gaussian distribution and the bell curve. .. The general form of its probability density function is-. Normal Distribution in . Statistics. The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena. . 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.. ). Let x. i. ~ N(. μ. i. , σ), then the probability density function is defined as. :. Letting: are . independent identical distributed with normal distribution, then the joint distribution of .