Normal Distribution The Bell Curve. Questions What are the parameters that drive the normal distribution? What does each control? Draw a picture to illustrate.

Slides:

Advertisements

Similar presentations

Section 5.1 Introduction to Normal Distributions and the Standard Normal Distribution.

Advertisements

Chapter 11- Confidence Intervals for Univariate Data Math 22 Introductory Statistics.

The Normal Distribution

Normal distribution. An example from class HEIGHTS OF MOTHERS CLASS LIMITS(in.)FREQUENCY

Stat350, Lecture#4 :Density curves and normal distribution Try to draw a smooth curve overlaying the histogram. The curve is a mathematical model for the.

Theoretical Probability Distributions We have talked about the idea of frequency distributions as a way to see what is happening with our data. We have.

The Normal Distribution

Normal Distributions What is a Normal Distribution? Why are Many Variables Normally Distributed? Why are Many Variables Normally Distributed? How Are Normal.

1.2: Describing Distributions

Measures of Dispersion

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 6-1 Chapter 6 The Normal Distribution and Other Continuous Distributions.

1.  Why understanding probability is important?  What is normal curve  How to compute and interpret z scores. 2.

Chap 6-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 6 Continuous Random Variables and Probability Distributions Statistics.

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 6-1 Chapter 6 The Normal Distribution and Other Continuous Distributions.

Review What you have learned in QA 128 Business Statistics I.

Central Tendency and Variability

Continuous Probability Distributions A continuous random variable can assume any value in an interval on the real line or in a collection of intervals.

Chapter 4 Continuous Random Variables and Probability Distributions

Probability Quantitative Methods in HPELS HPELS 6210.

Probability & the Normal Distribution

1 Normal Random Variables In the class of continuous random variables, we are primarily interested in NORMAL random variables. In the class of continuous.

Some Useful Continuous Probability Distributions.

Chapter 5 The Normal Curve. Histogram of Unemployment rates, States database.

Chapter 5 The Normal Curve. In This Presentation  This presentation will introduce The Normal Curve Z scores The use of the Normal Curve table (Appendix.

Copyright © 2012 by Nelson Education Limited. Chapter 4 The Normal Curve 4-1.

Sampling Distributions & Standard Error Lesson 7.

Normal Distribution. Intuition The sum of two dice The sum of two dice = 7 The total number of possibilities is : 6x6=36.

Education 793 Class Notes Normal Distribution 24 September 2003.

Math II UNIT QUESTION: Can real world data be modeled by algebraic functions? Standard: MM2D1, D2 Today’s Question: How is a normal distribution used to.

Modular 11 Ch 7.1 to 7.2 Part I. Ch 7.1 Uniform and Normal Distribution Recall: Discrete random variable probability distribution For a continued random.

Probability.  Provides a basis for thinking about the probability of possible outcomes  & can be used to determine how confident we can be in an effect.

The Standard Deviation as a Ruler and the Normal Model

Inference and Inferential Statistics Methods of Educational Research EDU 660.

Measures of central tendency are statistics that express the most typical or average scores in a distribution These measures are: The Mode The Median.

Statistics PSY302 Quiz One Spring A _____ places an individual into one of several groups or categories. (p. 4) a. normal curve b. spread c.

Determination of Sample Size: A Review of Statistical Theory

Thursday August 29, 2013 The Z Transformation. Today: Z-Scores First--Upper and lower real limits: Boundaries of intervals for scores that are represented.

Chapter 6 The Normal Distribution. 2 Chapter 6 The Normal Distribution Major Points Distributions and area Distributions and area The normal distribution.

Find out where you can find rand and randInt in your calculator. Write down the keystrokes.

Continuous Probability Distributions. A continuous random variable can assume any value in an interval on the real line or in a collection of intervals.

Sampling distributions rule of thumb…. Some important points about sample distributions… If we obtain a sample that meets the rules of thumb, then…

B AD 6243: Applied Univariate Statistics Data Distributions and Sampling Professor Laku Chidambaram Price College of Business University of Oklahoma.

Review Normal Distributions –Draw a picture. –Convert to standard normal (if necessary) –Use the binomial tables to look up the value. –In the case of.

Normal Distributions (aka Bell Curves, Gaussians) Spring 2010.

1 ES Chapter 3 ~ Normal Probability Distributions.

Normal Distribution S-ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.

Describing Data: Summary Measures. Identifying the Scale of Measurement Before you analyze the data, identify the measurement scale for each variable.

15.5 The Normal Distribution. A frequency polygon can be replaced by a smooth curve A data set that is normally distributed is called a normal curve.

Construction Engineering 221 Probability and statistics Normal Distribution.

Objective: To find probability using standard normal distribution.

The Normal Distribution

Normal Distribution and Parameter Estimation

Chapter 5 The Normal Curve.

Continuous Random Variables

Elementary Statistics: Picturing The World

The Normal Probability Distribution

Organizing and Displaying Data

Statistics PSY302 Review Quiz One Fall 2018

The normal distribution

Descriptive and inferential statistics. Confidence interval

Chapter 5 Continuous Random Variables and Probability Distributions

Quantitative Methods PSY302 Quiz Normal Curve Review February 6, 2017

CHAPTER 12 More About Regression

10-5 The normal distribution

Chapter 5 A Normal World.

Statistics PSY302 Review Quiz One Spring 2017

Normal Distribution The Bell Curve.

BUSINESS MARKET RESEARCH

Objective: To introduce the characteristics of normal distribution curve. Standard 5.10.

Chapter 5 Continuous Random Variables and Probability Distributions

Presentation transcript:

Normal Distribution The Bell Curve

Questions What are the parameters that drive the normal distribution? What does each control? Draw a picture to illustrate. Identify proportions of the normal, e.g., what percent falls above the mean? Between 1 and 2 SDs above the mean? What is the 95 percent confidence interval for the mean? How can the confidence interval be computed?

Function The Normal is a theoretical distribution specified by its two parameters. It is unimodal and symmetrical. The mode, median and mean are all just in the middle.

Function (2) There are only 2 variables that determine the curve, the mean and the variance. The rest are constants. 2 is 2. Pi is about 3.14, and e is the natural exponent (a number between 2 and 3). In z scores (M=0, SD=1), the equation becomes: (Negative exponent means that big |z| values give small function values in the tails.)

Areas and Probabilities Cumulative probability:

Areas and Probabilities (2) Probability of an Interval

Areas and Probabilities (3) Howell Table 3.1 shows a table with cumulative and split proportions zMean to z Larger F(a) Smaller Graph illustrates z = 1. The shaded portion is about 16 percent of the area under the curve.

Areas and Probabilities (3) Using the unit normal (z), we can find areas and probabilities for any normal distribution. Suppose X=120, M=100, SD=10. Then z=( )/10 = 2. About 98 % of cases fall below a score of 120 if the distribution is normal. In the normal, most (95%) are within 2 SD of the mean. Nearly everybody (99%) is within 3 SD of the mean.

Review What are the parameters that drive the normal distribution? What does each control? Draw a picture to illustrate. Identify proportions of the normal, e.g., what percent falls below a z of.4? What part falls below a z of –1?

Importance of the Normal Errors of measures, perceptions, predictions (residuals, etc.) X = T+e (true score theory) Distributions of real scores (e.g., height); if normal, can figure much Math implications (e.g., inferences re variance) Will have big role in statistics, described after the sampling distribution is introduced

Computer Exercise Get data from class (e.g., height in inches) Compute mean, SD, StErr of Mean in Excel Compute same in SAS PROC UNIVARIATE Show plots (stem-leaf & Boxplot) Show test of normality