The Central Limit Theorem. A water taxi sank in Baltimore’s Inner Harbor. Assume the weights of men is are normally distributed with a mean of 172.

Slides:

Advertisements

Similar presentations

The Central Limit Theorem

Advertisements

Central Limit Theorem Given:

Chapter 6 – Normal Probability Distributions

Sampling Distributions Welcome to inference!!!! Chapter 9.

Statistics Class 16 3/26/2012.

Section 5.2 ~ Properties of the Normal Distribution

Reminders: Parameter – number that describes the population Statistic – number that is computed from the sample data Mean of population = µ Mean of sample.

Sampling distributions. Example Take random sample of students. Ask “how many courses did you study for this past weekend?” Calculate a statistic, say,

5.3 The Central Limit Theorem. Roll a die 5 times and record the value of each roll. Find the mean of the values of the 5 rolls. Repeat this 250 times.

Slide Slide 1 Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley. Section 6-4 Sampling Distributions and Estimators Created by.

NORMAL CURVE Needed for inferential statistics. Find percentile ranks without knowing all the scores in the distribution. Determine probabilities.

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

PROBABILITY AND SAMPLES: THE DISTRIBUTION OF SAMPLE MEANS.

6-5 The Central Limit Theorem

Unit 8 Section 8-6.

Chapter 11: Random Sampling and Sampling Distributions

Density Curve A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: 1. The total area.

From Last week.

Slide Slide 1 Chapter 8 Sampling Distributions Mean and Proportion.

The Central Limit Theorem. 1. The random variable x has a distribution (which may or may not be normal) with mean and standard deviation. 2. Simple random.

Applications of the Normal Distribution

Section 7.1 The STANDARD NORMAL CURVE

AP Statistics Chapter 9 Notes.

Statistics Sampling Distributions

The distribution of heights of adult American men is approximately normal with mean 69 inches and standard deviation 2.5 inches. Use the rule.

Probability and Samples

And the Rule THE NORMAL DISTRIBUTION. SKEWED DISTRIBUTIONS & OUTLIERS.

Copyright © 2010, 2007, 2004 Pearson Education, Inc. Lecture Slides Elementary Statistics Eleventh Edition and the Triola Statistics Series by.

Chapter 6 Lecture 3 Sections: 6.4 – 6.5.

Normal Distributions.

Statistics Workshop Tutorial 8 Normal Distributions.

Please turn off cell phones, pagers, etc. The lecture will begin shortly. There will be a quiz at the end of today’s lecture. Friday’s lecture has been.

Copyright © 2010, 2007, 2004 Pearson Education, Inc. Chapter 6 Normal Probability Distributions 6-1 Review and Preview 6-2 The Standard Normal.

The Normal Distribution Chapter 6. Outline 6-1Introduction 6-2Properties of a Normal Distribution 6-3The Standard Normal Distribution 6-4Applications.

Chapter 10 – Sampling Distributions Math 22 Introductory Statistics.

Statistics 300: Elementary Statistics Section 6-5.

Probabilistic & Statistical Techniques Eng. Tamer Eshtawi First Semester Eng. Tamer Eshtawi First Semester

Distribution of the Sample Mean (Central Limit Theorem)

Slide Slide 1 Section 6-5 The Central Limit Theorem.

Section 6-5 The Central Limit Theorem. THE CENTRAL LIMIT THEOREM Given: 1.The random variable x has a distribution (which may or may not be normal) with.

The Central Limit Theorem 1. The random variable x has a distribution (which may or may not be normal) with mean and standard deviation. 2. Simple random.

Estimation Chapter 8. Estimating µ When σ Is Known.

Finding Probability Using the Normal Curve

1 Chapter 5. Section 5-5. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.

Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Lecture Slides Elementary Statistics Eleventh Edition and the Triola.

Chapter 6 Lecture 3 Sections: 6.4 – 6.5. Sampling Distributions and Estimators What we want to do is find out the sampling distribution of a statistic.

Chapter 18: The Central Limit Theorem Objective: To apply the Central Limit Theorem to the Normal Model CHS Statistics.

Vocab Normal, Standard Normal, Uniform, t Point Estimate Sampling distribution of the means Confidence Interval Confidence Level / α.

Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and.

Chapter 6 Lecture 2 Section: 6.3. Application of Normal Distribution In the previous section, we learned about finding the probability of a continuous.

{ Chapter 3 Lesson 9 Z-Scores  Z-Score- The value z when you take an x value in the data set, subtract the mean from it, then divide by the standard.

12 FURTHER MATHEMATICS STANDARD SCORES. Standard scores The 68–95–99.7% rule makes the standard deviation a natural measuring stick for normally distributed.

And distribution of sample means

The Central Limit Theorem

Sec. 7-5: Central Limit Theorem

Lecture Slides Elementary Statistics Twelfth Edition

SAMPLING DISTRIBUTION. Probability and Samples Sampling Distributions Central Limit Theorem Standard Error Probability of Sample Means.

Elementary Statistics

Quantitative Methods PSY302 Quiz Normal Curve Review February 7, 2018

Applications of the Normal Distribution

Chapter 6 Lecture 2 Section: 6.3.

Use the graph of the given normal distribution to identify μ and σ.

Warm Up Your textbook provides the following data on the height of men and women. Mean Std. Dev Men Women ) What is the z score.

Applications of the Normal Distribution

Central Limit Theorem Accelerated Math 3.

The Central Limit Theorem

The Normal Curve Section 7.1 & 7.2.

Lecture Slides Essentials of Statistics 5th Edition

Z-Scores 10/13/2015 Statistics Mr. DeOms

Warm Up Your textbook provides the following data on the height of men and women. Mean Std. Dev Men Women ) What is the z score.

Presentation transcript:

The Central Limit Theorem

A water taxi sank in Baltimore’s Inner Harbor. Assume the weights of men is are normally distributed with a mean of 172 lb. and a standard deviation of 29 lb. a.Find the probability that if an individual man is randomly selected, his weight will be greater than 175 lb.

The Central Limit Theorem A water taxi sank in Baltimore’s Inner Harbor. Assume the weights of men is are normally distributed with a mean of 172 lb. and a standard deviation of 29 lb. a.Find the probability that if an individual man is randomly selected, his weight will be greater than 175 lb. b.Find the probability that 20 randomly selected men will have a mean weight that is greater than 175 lb.

The Central Limit Theorem Recall the Rare Event rule for inferential Statistics If under a given assumption, the probability of a particular observed event is exceptionally small (such as less than 0.05), we conclude that the assumption is probably not correct.

The Central Limit Theorem The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a)If 1 pregnant woman is randomly selected, find the probability that her length of pregnancy is less than 260 days.

The Central Limit Theorem The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a)If 1 pregnant woman is randomly selected, find the probability that her length of pregnancy is less than 260 days. b)If 25 randomly selected women are put on a special diet just before they become pregnant, find the probability that their lengths of pregnancy have a mean that is less than 260 days.

The Central Limit Theorem The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a)If 1 pregnant woman is randomly selected, find the probability that her length of pregnancy is less than 260 days. b)If 25 randomly selected women are put on a special diet just before they become pregnant, find the probability that their lengths of pregnancy have a mean that is less than 260 days. c)If the 25 women do have a mean of less that 260 days, does it appear that the, does it appear that the diet has an effect on the length of pregnancy?

The Central Limit Theorem Membership in Mensa requires and IQ score of above Nine candidates take IQ tests, and their summary results indicated that their mean IQ score is 133. (IQ scores are normally distributed with a mean of 100 and a standard deviation of 15). a)If 1 person is randomly selected from the general population, find the probability of getting someone with an IQ score of at least 133.

The Central Limit Theorem Membership in Mensa requires and IQ score of above Nine candidates take IQ tests, and their summary results indicated that their mean IQ score is 133. (IQ scores are normally distributed with a mean of 100 and a standard deviation of 15). a)If 1 person is randomly selected from the general population, find the probability of getting someone with an IQ score of at least 133. b)If 9 people are randomly selected, find the probability that their mean IQ is at least 133.

The Central Limit Theorem Membership in Mensa requires and IQ score of above Nine candidates take IQ tests, and their summary results indicated that their mean IQ score is 133. (IQ scores are normally distributed with a mean of 100 and a standard deviation of 15). a)If 1 person is randomly selected from the general population, find the probability of getting someone with an IQ score of at least 133. b)If 9 people are randomly selected, find the probability that their mean IQ is at least 133. c)Although the summary results are available, the individual scores have been lost. Can is be concluded that all 9 candidates have IQ scores above so that they are all eligible for Mensa membership?

Group Quiz Tall Clubs International is a social organization for tall people. It has a requirement that men must be at least 74 in. tall, and women must be at least 70 in. tall. Heights of men are normally distributed with mean 69 in. and standard deviation 2.8 in. Heights of women are normally distributed with mean 63.6 in and standard deviation 2.5 in. a.What percentage of men meet that requirement? b. What percentage of women meet that requirement? c.Are the height requirements for men and women fair? Why or Why not? d.If the height requirements are changed for both men and women what would the new minimum heights be for both men and women?

Homework!! 6-3: 1-25 odd