*****CENTRAL LIMIT THEOREM (CLT)*****
|
|
- Darleen Banks
- 5 years ago
- Views:
Transcription
1 Sampling Distributions and CLT Day 5 *****CENTRAL LIMIT THEOREM (CLT)***** (One of the MOST important theorems in Statistics - KNOW AND UNDERSTAND THIS!!!!!!) Draw an SRS of size n from ANY population with mean μ and standard deviation σ. When n is LARGE, the sampling distribution of the sample mean is approximately NORMAL!!! with mean μ and standard deviation.
2 FOR EXAMPLE: KEEP IN MIND: 1. You MUST have a sample that is large enough to use the Central Limit Theorem ( 30 is usually good - we will spend more time on this later...). 2. Normal distributions are GREAT for calculating probabilities (like we have seen many times before) so the CLT is a VERY powerful tool
3 Central Limit Theorem Recap: If you take large enough sample sizes, then the sampling distribution will be normal in shape. 1) If the population is normal (or roughly normal), then you can take samples of any size 2) If the population is not normal, then you will need to take a large enough sample (generally n 30 is enough)
4 FOR EXAMPLE: An insurance company knows that the mean loss from fire for the entire population of homeowners is μ = $250 and the standard deviation of loss is σ = $1000. The distribution of losses is strongly skewed to the right: many policies have $0 loss, but a few have very large losses. a) What is the approximate probability the loss of one policy will be greater than $275? b) If the company sells 10,000 policies, what is the approximate probability that the average loss will be greater than $275?
5 Example 2: The scores of students on the ACT college entrance examination in 2001 had a mean score of 21 with standard deviation of 4.7. The distribution of scores is only roughly Normal. a) What is the approximate probability that a single student randomly chosen from all those taking the test scores 23 or lower? b) Now take an SRS of 50 students who took the test. What are the mean and standard deviation of the sample mean score of these 50 students? What is the approximate probability that the mean score of these students is 23 or lower? c) Which of your two Normal probability calculations in (a) and (b) is more accurate? Why?
6 Example 3: The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5 moths, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation of 0.7 moths. a) What are the mean and standard deviation of the average number of moths in 50 traps? b) Find the probability that the average number of moths in 50 traps is greater than 0.6 moths?
7 Example 4: In a recent year, there were about 4.8 million parents in the U.S. who received child support payments. The mean number of children in families receiving child support was 1.7 and the standard deviation was 0.8 a) What is the probability that a person has less than 2 children receiving child support payments? b) You randomly select 15 parents who receive child support and ask how many children in their custody are receiving child support payments. What is the probability that the mean of the sample is less than 2 children receiving child support payments?
8 Example 5: Suppose that we randomly select a sample of 64 measurements from a population having μ = 20 and σ = 4 a) Describe the sample of the sampling distribution of sample mean, x-bar. Do we need to know anything about the shape of the population? Why or why not? b) Find the mean and standard deviation of the sampling distribution of the sample mean. c) Can you find the probability that a single measurement will be greater than 21? If so, what is the probability?
9 d) Calculate the probability that we will obtain a sample mean greater than 21. e) 94% of the sample means will be below what value?
10 Example 6: David's ipod has about 10,000 songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviation of 60 seconds. a) Suppose we select a song at random from this population. Can we calculate the probability that the song is more than 4 minutes (240 seconds)? If so, calculate the probability. b) Suppose we selected a SRS of 10 songs from this population. Can we safely calculate the probability that the mean play time of x-bar is more than 4 minutes (240 seconds)? If so, calculate the probability.
11 c) Suppose we selected a SRS of 36 songs from this population. Can we safely calculate the probability that the mean play time of x-bar is more than 4 minutes (240 seconds)? If so, calculate the probability. d) Using a sample size of 36, the middle 70% of sample means will be in what range?
12 Example 7: A machine used to fill half-gallon-sized milk containers is regulated so that the amount of milk dispensed has a mean of 64 ounces and a standard deviation of 0.11 ounces. You randomly select 45 containers and carefully measure the contents. The sample mean of the containers is ounces. Does the machine need to be reset? Explain.
13 Example 8: The number of accidents per week at a hazardous intersection varies with μ = 2.2 and σ = 1.4. This distribution is not normal. a) Can we find the probability that a single week has less than 2 accidents? Why or Why not? b) Let x-bar be the mean number of accidents per week at the intersection during a year (52 weeks). What is the approximate distribution (mean and standard deviation) of x-bar according the Central Limit Theorem? c) What is the approximate probability that x-bar is less than 2?
14 d) What is the approximate probability that there are fewer than 100 accidents at the intersection in a year? (Hint: restate this event in terms of x-bar) e) 90% of the sample means for accidents will be in what range?
15 Homework: p. 275 #17, 25, 29, 33, 37, 42 Note: standard error of the mean = standard deviation of the sampling distribution of sample means
Activity #17b: Central Limit Theorem #2. 1) Explain the Central Limit Theorem in your own words.
Activity #17b: Central Limit Theorem #2 1) Explain the Central Limit Theorem in your own words. Importance of the CLT: You can standardize and use normal distribution tables to calculate probabilities
More information1. State Sales Tax. 2. Baggage Check
1. State Sales Tax A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6% with the additional revenue going to education. If 40% of all adults
More informationSTAT243 LS: Intro to Probability and Statistics Final Exam, Mar 20, 2017 KEY
STAT243 LS: Intro to Probability and Statistics Final Exam, Mar 20, 2017 KEY This is a 110-min exam. Students may use a page of note (front and back), and a calculator, but nothing else is allowed. 1.
More informationName: Period: Date: 1. Suppose we are interested in the average weight of chickens in America.
Name: Period: Date: Statistics Review MM4D1. Using simulation, students will develop the idea of the central limit theorem. MM4D2. Using student-generated data from random samples of at least 30 members,
More informationwork to get full credit.
Chapter 18 Review Name Date Period Write complete answers, using complete sentences where necessary.show your work to get full credit. MULTIPLE CHOICE. Choose the one alternative that best completes the
More informationConfidence Intervals: Review
University of Utah February 28, 2018 1 2 Law of Large Numbers Draw your samples from any population with finite mean µ. Then LLN says Law of Large Numbers Draw your samples from any population with finite
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Ch. 8 Sampling Distributions 8.1 Distribution of the Sample Mean 1 Describe the distribution of the sample mean: normal population. MULTIPLE CHOICE. Choose the one alternative that best completes the statement
More informationChapter 7 Study Guide: The Central Limit Theorem
Chapter 7 Study Guide: The Central Limit Theorem Introduction Why are we so concerned with means? Two reasons are that they give us a middle ground for comparison and they are easy to calculate. In this
More informationCentral Limit Theorem
Central Limit Theorem Lots of Samples 1 Homework Read Sec 6-5. Discussion Question pg 329 Do Ex 6-5 8-15 2 Objective Use the Central Limit Theorem to solve problems involving sample means 3 Sample Means
More informationAs you draw random samples of size n, as n increases, the sample means tend to be normally distributed.
The Central Limit Theorem The central limit theorem (clt for short) is one of the most powerful and useful ideas in all of statistics. The clt says that if we collect samples of size n with a "large enough
More informationUniform Probability Distribution. Continuous Random Variables &
Continuous Random Variables & What is a Random Variable? It is a quantity whose values are real numbers and are determined by the number of desired outcomes of an experiment. Is there any special Random
More informationName PID Section # (enrolled)
STT 315 - Lecture 3 Instructor: Aylin ALIN 04/02/2014 Midterm # 2 A Name PID Section # (enrolled) * The exam is closed book and 80 minutes. * You may use a calculator and the formula sheet that you brought
More informationChapter 9 & 10. Multiple Choice.
Chapter 9 & 10 Review Name Multiple Choice. 1. An agricultural researcher plants 25 plots with a new variety of corn. The average yield for these plots is X = 150 bushels per acre. Assume that the yield
More informationExample - Let X be the number of boys in a 4 child family. Find the probability distribution table:
Chapter8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables tthe value of the result of the probability experiment is a RANDOM VARIABLE. Example - Let X be the number
More information1. Variability in estimates and CLT
Unit3: Foundationsforinference 1. Variability in estimates and CLT Sta 101 - Fall 2015 Duke University, Department of Statistical Science Dr. Çetinkaya-Rundel Slides posted at http://bit.ly/sta101_f15
More informationI. Standard Error II. Standard Error III. Standard Error 2.54
1) Original Population: Match the standard error (I, II, or III) with the correct sampling distribution (A, B, or C) and the correct sample size (1, 5, or 10) I. Standard Error 1.03 II. Standard Error
More informationMLLunsford 1. Activity: Central Limit Theorem Theory and Computations
MLLunsford 1 Activity: Central Limit Theorem Theory and Computations Concepts: The Central Limit Theorem; computations using the Central Limit Theorem. Prerequisites: The student should be familiar with
More information1 Sampling Distributions
1 Sampling Distributions 1.1 Statistics and Sampling Distributions When a random sample is selected the numerical descriptive measures calculated from such a sample are called statistics. These statistics
More informationUsing the Central Limit Theorem It is important for you to understand when to use the CLT. If you are being asked to find the probability of the
Using the Central Limit Theorem It is important for you to understand when to use the CLT. If you are being asked to find the probability of the mean, use the CLT for the mean. If you are being asked to
More information8.1 Binomial Distributions
8.1 Binomial Distributions The Binomial Setting The 4 Conditions of a Binomial Setting: 1.Each observation falls into 1 of 2 categories ( success or fail ) 2 2.There is a fixed # n of observations. 3.All
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name The bar graph shows the number of tickets sold each week by the garden club for their annual flower show. ) During which week was the most number of tickets sold? ) A) Week B) Week C) Week 5
More informationChapter 6 Section Review day s.notebook. May 11, Honors Statistics. Aug 23-8:26 PM. 3. Review team test.
Honors Statistics Aug 23-8:26 PM 3. Review team test Aug 23-8:31 PM 1 Nov 27-10:28 PM 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 Nov 27-9:53 PM 2 May 8-7:44 PM May 1-9:09 PM 3 Dec 1-2:08 PM Sep
More informationThe Central Limit Theorem for Sample Means (Averages)
The Central Limit Theorem for Sample Means (Averages) By: OpenStaxCollege Suppose X is a random variable with a distribution that may be known or unknown (it can be any distribution). Using a subscript
More informationThe Central Limit Theorem: Homework
The Central Limit Theorem: Homework EXERCISE 1 X N(60, 9). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let X be the random variable of sums.
More informationThe Central Limit Theorem. Sec. 8.2: The Random Variable. it s Distribution. it s Distribution
The Central Limit Theorem Sec. 8.1: The Random Variable it s Distribution Sec. 8.2: The Random Variable it s Distribution X p and and How Should You Think of a Random Variable? Imagine a bag with numbers
More informationThe Central Limit Theorem: Homework
The Central Limit Theorem: Homework EXERCISE 1 X N(60, 9). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let X be the random variable of sums.
More informationThe binomial distribution p314
The binomial distribution p314 Example: A biased coin (P(H) = p = 0.6) ) is tossed 5 times. Let X be the number of H s. Fine P(X = 2). This X is a binomial r. v. The binomial setting p314 1. There are
More informationAP * Statistics Review
AP * Statistics Review Normal Models and Sampling Distributions Teacher Packet AP* is a trademark of the College Entrance Examination Board. The College Entrance Examination Board was not involved in the
More informationChapter 7. Sampling Distributions and the Central Limit Theorem
Chapter 7. Sampling Distributions and the Central Limit Theorem 1 Introduction 2 Sampling Distributions related to the normal distribution 3 The central limit theorem 4 The normal approximation to binomial
More informationExample - Let X be the number of boys in a 4 child family. Find the probability distribution table:
Chapter7 Probability Distributions and Statistics Distributions of Random Variables tthe value of the result of the probability experiment is a RANDOM VARIABLE. Example - Let X be the number of boys in
More informationDistribution of the Sample Mean
Distribution of the Sample Mean MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2018 Experiment (1 of 3) Suppose we have the following population : 4 8 1 2 3 4 9 1
More informationand µ Asian male > " men
A.P. Statistics Sampling Distributions and the Central Limit Theorem Definitions A parameter is a number that describes the population. A parameter always exists but in practice we rarely know its value
More informationHonors Statistics. Daily Agenda
Honors Statistics Aug 23-8:26 PM Daily Agenda 1. Review OTL C6#7 emphasis Normal Distributions Aug 23-8:31 PM 1 1. Multiple choice: Select the best answer for Exercises 65 and 66, which refer to the following
More informationLecture 3. Sampling distributions. Counts, Proportions, and sample mean.
Lecture 3 Sampling distributions. Counts, Proportions, and sample mean. Statistical Inference: Uses data and summary statistics (mean, variances, proportions, slopes) to draw conclusions about a population
More informationChapter 7: Sampling Distributions Chapter 7: Sampling Distributions
Chapter 7: Sampling Distributions Objectives: Students will: Define a sampling distribution. Contrast bias and variability. Describe the sampling distribution of a proportion (shape, center, and spread).
More informationThe Central Limit Theorem: Homework
EERCISE 1 The Central Limit Theorem: Homework N(60, 9). Suppose that you form random samples of 25 from this distribution. Let be the random variable of averages. Let be the random variable of sums. For
More informationCentral Limit Theorem: Homework
Connexions module: m16952 1 Central Limit Theorem: Homework Susan Dean Barbara Illowsky, Ph.D. This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License
More informationA random variable (r. v.) is a variable whose value is a numerical outcome of a random phenomenon.
Chapter 14: random variables p394 A random variable (r. v.) is a variable whose value is a numerical outcome of a random phenomenon. Consider the experiment of tossing a coin. Define a random variable
More informationMaking Sense of Cents
Name: Date: Making Sense of Cents Exploring the Central Limit Theorem Many of the variables that you have studied so far in this class have had a normal distribution. You have used a table of the normal
More informationRandom Variables CHAPTER 6.3 BINOMIAL AND GEOMETRIC RANDOM VARIABLES
Random Variables CHAPTER 6.3 BINOMIAL AND GEOMETRIC RANDOM VARIABLES Essential Question How can I determine whether the conditions for using binomial random variables are met? Binomial Settings When the
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Use the Central Limit Theorem to find the indicated probability. The sample size is n,
More informationAP STATISTICS Name: Period: Review Unit VI Probability Models and Sampling Distributions
AP STATISTICS Name: Period: Review Unit VI Probability Models and Sampling Distributions Show all work and reasoning. 1. Professional football players in the NFL have a distribution of salaries that is
More informationLecture 9. Probability Distributions. Outline. Outline
Outline Lecture 9 Probability Distributions 6-1 Introduction 6- Probability Distributions 6-3 Mean, Variance, and Expectation 6-4 The Binomial Distribution Outline 7- Properties of the Normal Distribution
More informationProblem Set 08 Sampling Distribution of Sample Mean
Problem Set 08 Sampling Distribution of Sample Mean MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the requested probability. 1) The table reports
More informationChapter Seven. The Normal Distribution
Chapter Seven The Normal Distribution 7-1 Introduction Many continuous variables have distributions that are bellshaped and are called approximately normally distributed variables, such as the heights
More informationLecture 9. Probability Distributions
Lecture 9 Probability Distributions Outline 6-1 Introduction 6-2 Probability Distributions 6-3 Mean, Variance, and Expectation 6-4 The Binomial Distribution Outline 7-2 Properties of the Normal Distribution
More informationExample. Chapter 8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables
Chapter 8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables You are dealt a hand of 5 cards. Find the probability distribution table for the number of hearts. Graph
More informationSampling. Marc H. Mehlman University of New Haven. Marc Mehlman (University of New Haven) Sampling 1 / 20.
Sampling Marc H. Mehlman marcmehlman@yahoo.com University of New Haven (University of New Haven) Sampling 1 / 20 Table of Contents 1 Sampling Distributions 2 Central Limit Theorem 3 Binomial Distribution
More informationChapter 7. Sampling Distributions and the Central Limit Theorem
Chapter 7. Sampling Distributions and the Central Limit Theorem 1 Introduction 2 Sampling Distributions related to the normal distribution 3 The central limit theorem 4 The normal approximation to binomial
More informationSampling Distributions
AP Statistics Ch. 7 Notes Sampling Distributions A major field of statistics is statistical inference, which is using information from a sample to draw conclusions about a wider population. Parameter:
More informationSection3-2: Measures of Center
Chapter 3 Section3-: Measures of Center Notation Suppose we are making a series of observations, n of them, to be exact. Then we write x 1, x, x 3,K, x n as the values we observe. Thus n is the total number
More information6 Central Limit Theorem. (Chs 6.4, 6.5)
6 Central Limit Theorem (Chs 6.4, 6.5) Motivating Example In the next few weeks, we will be focusing on making statistical inference about the true mean of a population by using sample datasets. Examples?
More informationSTAT Chapter 6: Sampling Distributions
STAT 515 -- Chapter 6: Sampling Distributions Definition: Parameter = a number that characterizes a population (example: population mean ) it s typically unknown. Statistic = a number that characterizes
More informationMEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS MIDTERM EXAM - STATISTICS FALL 2014, SECTION 005
MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS MIDTERM EXAM - STATISTICS 2550 - FALL 2014, SECTION 005 Instructor: A. Oyet Date: October 16, 2014 Name(Surname First): Student
More informationChapter 7 Sampling Distributions and Point Estimation of Parameters
Chapter 7 Sampling Distributions and Point Estimation of Parameters Part 1: Sampling Distributions, the Central Limit Theorem, Point Estimation & Estimators Sections 7-1 to 7-2 1 / 25 Statistical Inferences
More information22.2 Shape, Center, and Spread
Name Class Date 22.2 Shape, Center, and Spread Essential Question: Which measures of center and spread are appropriate for a normal distribution, and which are appropriate for a skewed distribution? Eplore
More informationChapter Six Probability Distributions
6.1 Probability Distributions Discrete Random Variable Chapter Six Probability Distributions x P(x) 2 0.08 4 0.13 6 0.25 8 0.31 10 0.16 12 0.01 Practice. Construct a probability distribution for the number
More informationWhat type of distribution is this? tml
Warm Up Calculate the average Broncos score for the 2013 Season! 24, 27, 10, 10, 34, 37, 20, 51, 35, 31, 27, 28, 45, 33, 35, 52, 52, 37, 41, 49, 24, 26 What type of distribution is this? http://www.mathsisfun.com/data/quincunx.h
More informationSection 6.5. The Central Limit Theorem
Section 6.5 The Central Limit Theorem Idea Will allow us to combine the theory from 6.4 (sampling distribution idea) with our central limit theorem and that will allow us the do hypothesis testing in the
More informationSTT 315 Practice Problems Chapter 3.7 and 4
STT 315 Practice Problems Chapter 3.7 and 4 Answer the question True or False. 1) The number of children in a family can be modelled using a continuous random variable. 2) For any continuous probability
More informationUniversity of California, Los Angeles Department of Statistics. The central limit theorem The distribution of the sample mean
University of California, Los Angeles Department of Statistics Statistics 12 Instructor: Nicolas Christou First: Population mean, µ: The central limit theorem The distribution of the sample mean Sample
More informationName PID Section # (enrolled)
STT 315 - Lecture 3 Instructor: Aylin ALIN 02/19/2014 Midterm # 1 A Name PID Section # (enrolled) * The exam is closed book and 80 minutes. * You may use a calculator and the formula sheet that you brought
More informationExercise Questions. Q7. The random variable X is known to be uniformly distributed between 10 and
Exercise Questions This exercise set only covers some topics discussed after the midterm. It does not mean that the problems in the final will be similar to these. Neither solutions nor answers will be
More informationCover Page Homework #8
MODESTO JUNIOR COLLEGE Department of Mathematics MATH 134 Fall 2011 Problem 11.6 Cover Page Homework #8 (a) What does the population distribution describe? (b) What does the sampling distribution of x
More informationNormal Curves & Sampling Distributions
Chapter 7 Name Normal Curves & Sampling Distributions Section 7.1 Graphs of Normal Probability Distributions Objective: In this lesson you learned how to graph a normal curve and apply the empirical rule
More informationCHAPTER 5 SAMPLING DISTRIBUTIONS
CHAPTER 5 SAMPLING DISTRIBUTIONS Sampling Variability. We will visualize our data as a random sample from the population with unknown parameter μ. Our sample mean Ȳ is intended to estimate population mean
More informationSAMPLING DISTRIBUTIONS. Chapter 7
SAMPLING DISTRIBUTIONS Chapter 7 7.1 How Likely Are the Possible Values of a Statistic? The Sampling Distribution Statistic and Parameter Statistic numerical summary of sample data: p-hat or xbar Parameter
More information4.2 Probability Distributions
4.2 Probability Distributions Definition. A random variable is a variable whose value is a numerical outcome of a random phenomenon. The probability distribution of a random variable tells us what the
More informationSampling Distributions
Al Nosedal. University of Toronto. Fall 2017 October 26, 2017 1 What is a Sampling Distribution? 2 3 Sampling Distribution The sampling distribution of a statistic is the distribution of values taken by
More informationCh 8 One Population Confidence Intervals
Ch 8 One Population Confidence Intervals Section A: Multiple Choice C 1. A single number used to estimate a population parameter is a. the confidence interval b. the population parameter c. a point estimate
More informationAP Stats. Ch.7 Competition MULTUPLE CHIUCE. Choose the one alternative that best completes the statement or answers the question.
AP Stats. Ch.7 Competition MULTUPLE CHIUCE. Choose the one alternative that best completes the statement or answers the question. Determine whether the Normal model may be used to describe the distribution
More informationHonors Statistics. 3. Review OTL C6#6. emphasis Normal Distributions. Chapter 6 Section 2 Day s.notebook. May 05, 2016.
Honors Statistics Aug 23-8:26 PM 3. Review OTL C6#6 emphasis Normal Distributions Aug 23-8:31 PM 1 Nov 21-8:16 PM Rainy days Imagine that we randomly select a day from the past 10 years. Let X be the recorded
More informationModule 4: Probability
Module 4: Probability 1 / 22 Probability concepts in statistical inference Probability is a way of quantifying uncertainty associated with random events and is the basis for statistical inference. Inference
More informationIn a binomial experiment of n trials, where p = probability of success and q = probability of failure. mean variance standard deviation
Name In a binomial experiment of n trials, where p = probability of success and q = probability of failure mean variance standard deviation µ = n p σ = n p q σ = n p q Notation X ~ B(n, p) The probability
More informationSTA 320 Fall Thursday, Dec 5. Sampling Distribution. STA Fall
STA 320 Fall 2013 Thursday, Dec 5 Sampling Distribution STA 320 - Fall 2013-1 Review We cannot tell what will happen in any given individual sample (just as we can not predict a single coin flip in advance).
More informationTest 6A AP Statistics Name:
Test 6A AP Statistics Name: Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. A marketing survey compiled data on the number of personal computers in households. If X = the
More informationProbability & Sampling The Practice of Statistics 4e Mostly Chpts 5 7
Probability & Sampling The Practice of Statistics 4e Mostly Chpts 5 7 Lew Davidson (Dr.D.) Mallard Creek High School Lewis.Davidson@cms.k12.nc.us 704-786-0470 Probability & Sampling The Practice of Statistics
More informationThe Central Limit Theorem
Section 6-5 The Central Limit Theorem I. Sampling Distribution of Sample Mean ( ) Eample 1: Population Distribution Table 2 4 6 8 P() 1/4 1/4 1/4 1/4 μ (a) Find the population mean and population standard
More informationPRINTABLE VERSION. Quiz 6. Suppose that x is normally distributed with a mean of 20 and a standard deviation of 3. What is P(16.91 x 24.59)?
PRINTABLE VERSION Quiz 6 Question 1 Suppose that x is normally distributed with a mean of 20 and a standard deviation of 3. What is P(16.91 x 24.59)? a) 0.348 b) 0.438 c) 0.353 d) 0.437 e) 0.785 Question
More informationNormal Cumulative Distribution Function (CDF)
The Normal Model 2 Solutions COR1-GB.1305 Statistics and Data Analysis Normal Cumulative Distribution Function (CDF 1. Suppose that an automobile muffler is designed so that its lifetime (in months is
More informationSTATISTICS - CLUTCH CH.9: SAMPLING DISTRIBUTIONS: MEAN.
!! www.clutchprep.com SAMPLING DISTRIBUTIONS (MEANS) As of now, the normal distributions we have worked with only deal with the population of observations Example: What is the probability of randomly selecting
More informationFINAL REVIEW W/ANSWERS
FINAL REVIEW W/ANSWERS ( 03/15/08 - Sharon Coates) Concepts to review before answering the questions: A population consists of the entire group of people or objects of interest to an investigator, while
More informationSection The Sampling Distribution of a Sample Mean
Section 5.2 - The Sampling Distribution of a Sample Mean Statistics 104 Autumn 2004 Copyright c 2004 by Mark E. Irwin The Sampling Distribution of a Sample Mean Example: Quality control check of light
More informationSampling and sampling distribution
Sampling and sampling distribution September 12, 2017 STAT 101 Class 5 Slide 1 Outline of Topics 1 Sampling 2 Sampling distribution of a mean 3 Sampling distribution of a proportion STAT 101 Class 5 Slide
More informationECON 214 Elements of Statistics for Economists 2016/2017
ECON 214 Elements of Statistics for Economists 2016/2017 Topic The Normal Distribution Lecturer: Dr. Bernardin Senadza, Dept. of Economics bsenadza@ug.edu.gh College of Education School of Continuing and
More informationStandard Normal, Inverse Normal and Sampling Distributions
Standard Normal, Inverse Normal and Sampling Distributions Section 5.5 & 6.6 Cathy Poliak, Ph.D. cathy@math.uh.edu Office in Fleming 11c Department of Mathematics University of Houston Lecture 9-3339 Cathy
More informationUniversity of California, Los Angeles Department of Statistics
University of California, Los Angeles Department of Statistics Statistics 13 Instructor: Nicolas Christou The central limit theorem The distribution of the sample proportion The distribution of the sample
More informationCHAPTER 6 Random Variables
CHAPTER 6 Random Variables 6.3 Binomial and Geometric Random Variables The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Binomial and Geometric Random
More informationSection Random Variables and Histograms
Section 3.1 - Random Variables and Histograms Definition: A random variable is a rule that assigns a number to each outcome of an experiment. Example 1: Suppose we toss a coin three times. Then we could
More informationA random variable (r. v.) is a variable whose value is a numerical outcome of a random phenomenon.
Chapter 14: random variables p394 A random variable (r. v.) is a variable whose value is a numerical outcome of a random phenomenon. Consider the experiment of tossing a coin. Define a random variable
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or Solve the problem. 1. Find forα=0.01. A. 1.96 B. 2.575 C. 1.645 D. 2.33 2.Whatistheconfidencelevelofthefolowingconfidenceintervalforμ?
More informationNOTES: Chapter 4 Describing Data
NOTES: Chapter 4 Describing Data Intro to Statistics COLYER Spring 2017 Student Name: Page 2 Section 4.1 ~ What is Average? Objective: In this section you will understand the difference between the three
More information(j) Find the first quartile for a standard normal distribution.
Examples for Chapter 5 Normal Probability Distributions Math 1040 1 Section 5.1 1. Heights of males at a certain university are approximately normal with a mean of 70.9 inches and a standard deviation
More informationThe Binomial Probability Distribution
The Binomial Probability Distribution MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2017 Objectives After this lesson we will be able to: determine whether a probability
More informationSection 6.3 Binomial and Geometric Random Variables
Section 6.3 Binomial and Geometric Random Variables Mrs. Daniel AP Stats Binomial Settings A binomial setting arises when we perform several independent trials of the same chance process and record the
More informationChapter 6: Random Variables
Chapter 6: Random Variables Section 6.3 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 6 Random Variables 6.1 Discrete and Continuous Random Variables 6.2 Transforming and
More informationTest 7A AP Statistics Name: Directions: Work on these sheets.
Test 7A AP Statistics Name: Directions: Work on these sheets. Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. Suppose X is a random variable with mean µ. Suppose we observe
More informationNormal distribution. We say that a random variable X follows the normal distribution if the probability density function of X is given by
Normal distribution The normal distribution is the most important distribution. It describes well the distribution of random variables that arise in practice, such as the heights or weights of people,
More informationChapter 15: Sampling distributions
=true true Chapter 15: Sampling distributions Objective (1) Get "big picture" view on drawing inferences from statistical studies. (2) Understand the concept of sampling distributions & sampling variability.
More informationStatistics for Managers Using Microsoft Excel 7 th Edition
Statistics for Managers Using Microsoft Excel 7 th Edition Chapter 7 Sampling Distributions Statistics for Managers Using Microsoft Excel 7e Copyright 2014 Pearson Education, Inc. Chap 7-1 Learning Objectives
More information