The Normal Distribution…

Slides:

Advertisements

Similar presentations

Chapter 5 Some Key Ingredients for Inferential Statistics: The Normal Curve, Probability, and Population Versus Sample.

Advertisements

The Normal Distribution

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Trapezoidal Rule Section 5.5.

Lesson #17 Sampling Distributions. The mean of a sampling distribution is called the expected value of the statistic. The standard deviation of a sampling.

T T07-01 Sample Size Effect – Normal Distribution Purpose Allows the analyst to analyze the effect that sample size has on a sampling distribution.

BPS - 3rd Ed. Chapter 131 Confidence intervals: the basics.

Area of a single trapezoid = h

Numerical Integration

Numerical Integration Approximating Definite Integral.

Today’s class Numerical Integration Newton-Cotes Numerical Methods

MAT 1235 Calculus II Section 7.7 Approximate (Numerical) Integration

1 Numerical Analysis Lecture 12 Numerical Integration Dr. Nader Okasha.

4.6 Numerical Integration Trapezoid and Simpson’s Rules.

4.6 Numerical Integration. The Trapezoidal Rule One method to approximate a definite integral is to use n trapezoids.

1 Numerical Integration Section Why Numerical Integration? Let’s say we want to evaluate the following definite integral:

In 2009, the mean mathematics score was 21 with a standard deviation of 5.3 for the ACT mathematics section. ReferenceReference Draw the normal curve in.

Normal Distributions Z Transformations Central Limit Theorem Standard Normal Distribution Z Distribution Table Confidence Intervals Levels of Significance.

Correlation and Prediction Error The amount of prediction error is associated with the strength of the correlation between X and Y.

Chapter 10 – Sampling Distributions Math 22 Introductory Statistics.

22 - 3/3/2000AME 150L1 Numerical Integration /3/2000AME 150L2 What You Know 125 Calculus I (4) Limits; continuity, derivatives and applications;

Statistics 300: Elementary Statistics Section 6-5.

BPS - 3rd Ed. Chapter 131 Confidence Intervals: The Basics.

§ 5.3 Normal Distributions: Finding Values. Probability and Normal Distributions If a random variable, x, is normally distributed, you can find the probability.

Numerical Integration

Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 1 Estimates and Sample Sizes Chapter 6 M A R I O F. T R I O L A Copyright © 1998,

1). Standard Deviation Normal Curve Standard Deviation mean.

6. Numerical Integration 6.1 Definition of numerical integration. 6.2 Reasons to use numerical integration. 6.3 Formulas of numerical Integration. 6.4.

WELCOME TO MATH 3 Please begin reading the syllabus on your desk!

Slide 6- 1 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Active Learning Lecture Slides For use with Classroom Response.

Normal Probability Distributions Chapter 5. § 5.2 Normal Distributions: Finding Probabilities.

m/sampling_dist/index.html.

MATH Section 4.4.

LESSON 5 - STATISTICS & RESEARCH STATISTICS – USE OF MATH TO ORGANIZE, SUMMARIZE, AND INTERPRET DATA.

Characteristics of Normal Distribution symmetric with respect to the mean mean = median = mode 100% of the data fits under the curve.

Trapezoidal Rule & Simpsons Rule AP Calculus Mrs. Mongold.

Numerical Integration using Trapezoidal Rule

Quadrature – Concepts (numerical integration) Don Allen.

Chapter 4 – Statistics II

5.5 Numerical Integration

1. According to ______ the larger the sample, the closer the sample mean is to the population mean. (p. 251) Murphy’s law the law of large numbers the.

Use the Midpoint Rule to approximate the given integral with the specified value of n. Compare your result to the actual value and find the error in the.

Midpoint and Trapezoidal Rules

Section 7.1 Central Limit Theorem

MTH1170 Numeric Integration

Inference: Conclusion with Confidence

5.5 Trapezoidal Rule.

Statistical Inference

3.5 z-scores & the Empirical Rule

AP Statistics Empirical Rule.

Numerical Integration Formulas

Statistics and Science

MATH 2311 Section 4.4.

Lecture Slides Elementary Statistics Twelfth Edition

Lecture Slides Elementary Statistics Twelfth Edition

Using the Normal Distribution

5.5 Numerical Integration

Using integrals to find area works extremely well as long as we can find the antiderivative of the function. Sometimes, the function is too complicated.

Chapter 6 Applications of Derivatives Section 6.5 Trapezoidal Rule.

CHAPTER 15 SUMMARY Chapter Specifics

How do I use normal distributions in finding probabilities?

5.5 Numerical Integration

Central Limit Theorem Accelerated Math 3.

5.5 Numerical Integration

A note about z-scores: All z-scores do not follow a Normal distribution. A z-score simply tells how many standard deviations a value is from the mean,

Introduction to Inference

Numerical Integration

How Confident Are You?.

Statistics 101 Chapter 8 Section 8.1 c and d.

Presentation transcript:

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. For example…. In a Math 205 Midterm exam the average score was 65% and the standard deviation was 10%. Estimate the fraction of the class that scored higher than 85%.

Where do z-values come from? Easiest way is to numerically integrate

Numerical Integration Methods Trapezoidal – approximate the function by a series of trapezoids Simpson’s Method – approximate the function by a series of parabolas! Error Simpson’s Rule is very robust and an often used numerical scheme