Normal Random Variables
|
|
- Hollie Ashlynn Leonard
- 5 years ago
- Views:
Transcription
1 Normal Random Variables In the continuous model there is no table. The distribution is described by a graph of a positive function and the probabilities are found using the areas under between that function and x-axis on a particular range. This function is called probability density function. Example 1. The height of 18-year-old male is distributed approximately according to the following density, This seems on average 70 inches with a standard deviation of 3 inches. We shall learn how to recognize this later. If we are interested in calculating the chance that a random 18-year-old would be anywhere between 72 and 76 inches tall we would need to calculate the following area:
2 *** The chance the height is between 65 and 70 inches is the following area:
3 This seems simple enough but we do not have knowledge to calculate these areas! Definition Random Variable with the density given by 2 x µ σ f( x) = e for any real x (1.1) 2 2πσ where µ is real number and σ > 0 (positive real number), is called Normal Random 2 N µσ,. Variable with parameters µ and σ and often denoted by ( ) In case of ( 0,1) N we call the variable Standard Normal Random Variable and often denote with Z. Although this variable has no value as a particular model, it does serve for standardization and once we learn to calculate the areas under the density curve of Standard Normal Random Variable we will be able to calculate the areas under any normal density.
4 Example 2. What is the chance that Z is less than 1.3. We write that as P( Z < 1.3) following area:. This is the We use textbook tables (attend the class): P Z < ( ) Example 3. What is the chance that Z value is between 0 and 1? P 0< Z < 1. The area is shown below. We write that as ( ) We use the textbook tables (attend the lecture!) to determine that P 0 < Z < = ( )
5 Example 4. P Z > The area is: Evaluate ( ) From the textbook tables again: P Z > = Evaluate ( 0.37 Z 0.82) ( ) Example 5. P < <. This is the following area: From the tables: P( Z ) 0.37 < < =
6 Example 6. P 1.47 < Z < Evaluate ( ) From the tables: P( Z ) 1.47 < < = *** Notable features of the graph of pdf for Standard Normal RV are: 1. Obviously the total area under the curve is 1. This is forced by the meaning and it can be shown using calculus methods. 2. Bell shaped curve with maximum at x = 0 and symmetrical about that line. This is easy to see using calculus from the expression for the function. 3. Inflexions at x = ± 1. We know this from calculus as well. 4. Empirical rule This will be explained in the class, attend the lecture! Homework: Check online
7 Standardization For general normal random variable the properties 1-4 from the previous section are analogous: 1. The total area under the curve is Bell shaped curve with maximum at x = µ (where µ is the mean of the variable) and symmetrical about that line. 3. Inflexions at x = ± σ where σ is the standard deviation of the variable. 4. Empirical rule holds as well. The only difference between various normal distributions is the scale, check the following two images:
8 Therefore to calculate the areas under the curve of general normal density we need to rescale the numerical values to z-values according to the following formula: z value = x µ σ For example, in example 1, the z-value of height of 76 inches is x µ z value = = = 2. σ 3 Example 7. What is the probability that a random 18-year-old male is anywhere between 70 and 76 inches tall? Solution: The question is formulated first in terms of original random variable, then re-scaled to z- values and then we use the tables, P ( 70 X 76) = P Z 3 3 ( 0 Z 2) = P The answer is approximately 48%.
9 Example 8. The average length of adult garden snake is 7 inches while the variable (length of a random garden snake) has standard deviation of 1.5 inches. Assuming normal distribution, what is the chance a random garden snake would be longer than 8 inches? P ( 8 < X ) 8 7 = P < Z 1. 5 ( 0.67 Z) P < The answer is approximately 25%. Example 9. The average IQ of general population is 100 while the random variable (IQ of a random person) has a standard deviation of 15. The average IQ of 9-year-old children in Tokio is 109. What percentage of general population is less intelligent than an average 9-year-old in Tokio? P ( X < 109) = P Z < 15 ( Z 0.6) = P < The answer is about 73%. Example 10. The average white blood cell count per cubic millimeter of whole blood is The standard deviation of white blood cell count per cubic millimeter is Assume normal distribution. What percentage of random lab tests shows the WCBC between 5,000 and 10,000?
10 P ( 5000 X < 10000) = P Z ( 1.43 Z 1.43) P < < Approximately 85%. Homework: Check online.
Normal Random Variables
Normal Random Variables Continuous random variables have uncountable many values. The distribution is described by a graph of a positive function and the probabilities are found using the areas under between
More informationCalculus with Algebra and Trigonometry II Lecture 21 Probability applications
Calculus with Algebra and Trigonometry II Lecture 21 Probability applications Apr 16, 215 Calculus with Algebra and Trigonometry II Lecture 21Probability Apr applications 16, 215 1 / 1 Histograms The distribution
More informationChapter 2: Summarizing and Graphing Data
Chapter 2: Summarizing and Graphing Data 9 Chapter 2: Summarizing and Graphing Data Section 2-2 1. No. For each class, the frequency tells us how many values fall within the given range of values, but
More informationChapter 8 Sampling Distributions Defn Defn
1 Chapter 8 Sampling Distributions Defn: Sampling error is the error resulting from using a sample to infer a population characteristic. Example: We want to estimate the mean amount of Pepsi-Cola in 12-oz.
More informationStatistics lecture 3. Bell-Shaped Curves and Other Shapes
Statistics lecture 3 Bell-Shaped Curves and Other Shapes Goals for lecture 3 Realize many measurements in nature follow a bell-shaped ( normal ) curve Understand and learn to compute a standardized score
More informationContinuous RVs. 1. Suppose a random variable X has the following probability density function: π, zero otherwise. f ( x ) = sin x, 0 < x < 2
STAT 4 Exam I Continuous RVs Fall 27 Practice. Suppose a random variable X has the following probability density function: f ( x ) = sin x, < x < 2 π, zero otherwise. a) Find P ( X < 4 π ). b) Find µ =
More informationa table or a graph or an equation.
Topic (8) POPULATION DISTRIBUTIONS 8-1 So far: Topic (8) POPULATION DISTRIBUTIONS We ve seen some ways to summarize a set of data, including numerical summaries. We ve heard a little about how to sample
More informationIntroductory Statistics
Introductory Statistics OpenStax Rice University 6100 Main Street MS-375 Houston, Texas 77005 To learn more about OpenStax, visit http://openstaxcollege.org. Individual print copies and bulk orders can
More informationMeasures of Central Tendency and their dispersion and applications. Acknowledgement: Dr Muslima Ejaz
Measures of Central Tendency and their dispersion and applications Acknowledgement: Dr Muslima Ejaz LEARNING OBJECTIVES: Compute and distinguish between the uses of measures of central tendency: mean,
More information8.4 Application to Economics/ Biology & Probability
8.4 Application to Economics/ Biology & 8.5 - Probability http://classic.hippocampus.org/course_locat or?course=general+calculus+ii&lesson=62&t opic=2&width=800&height=684&topictitle= Costs+&+probability&skinPath=http%3A%2F%
More information9/19/2012. PSY 511: Advanced Statistics for Psychological and Behavioral Research 1
PSY 511: Advanced Statistics for Psychological and Behavioral Research 1 The aspect of the data we want to describe/measure is relative position z scores tell us how many standard deviations above or below
More informationLecture 8: Chapter 4, Section 4 Quantitative Variables (Normal)
Lecture 8: Chapter 4, Section 4 Quantitative Variables (Normal) 68-95-99.7 Rule Normal Curve z-scores Cengage Learning Elementary Statistics: Looking at the Big Picture 1 Looking Back: Review 4 Stages
More informationHomework 7. Name: ID# Section
Homework 7 Name: ID# Section 1 Find the probabilities for each of the following using the standard normal distribution. 1. P(0 < z < 1.69) 2. P(-1.57 < z < 0) 3. P(z > 1.16) 4. P(z < -1.77) 5. P(-2.46
More informationThe Chi-Square Distributions
MATH 03 The Chi-Square Distributions Dr. Neal, Spring 009 The chi-square distributions can be used in statistics to analyze the standard deviation of a normally distributed measurement and to test the
More informationMath 1040 Sample Final Examination. Problem Points Score Total 200
Name: Math 1040 Sample Final Examination Relax and good luck! Problem Points Score 1 25 2 25 3 25 4 25 5 25 6 25 7 25 8 25 Total 200 1. (25 points) The systolic blood pressures of 20 elderly patients in
More informationThe Chi-Square Distributions
MATH 183 The Chi-Square Distributions Dr. Neal, WKU The chi-square distributions can be used in statistics to analyze the standard deviation σ of a normally distributed measurement and to test the goodness
More informationMath 223 Lecture Notes 3/15/04 From The Basic Practice of Statistics, bymoore
Math 223 Lecture Notes 3/15/04 From The Basic Practice of Statistics, bymoore Chapter 3 continued Describing distributions with numbers Measuring spread of data: Quartiles Definition 1: The interquartile
More informationMeasurement & Lab Equipment
Measurement & Lab Equipment Abstract This lab reviews the concept of scientific measurement, which you will employ weekly throughout this course. Specifically, we will review the metric system so that
More informationDETERMINE whether the conditions for performing inference are met. CONSTRUCT and INTERPRET a confidence interval to compare two proportions.
Section 0. Comparing Two Proportions Learning Objectives After this section, you should be able to DETERMINE whether the conditions for performing inference are met. CONSTRUCT and INTERPRET a confidence
More informationThe Normal Distribuions
The Normal Distribuions Sections 5.4 & 5.5 Cathy Poliak, Ph.D. cathy@math.uh.edu Office in Fleming 11c Department of Mathematics University of Houston Lecture 15-3339 Cathy Poliak, Ph.D. cathy@math.uh.edu
More informationEssential Question: What are the standard intervals for a normal distribution? How are these intervals used to solve problems?
Acquisition Lesson Planning Form Plan for the Concept, Topic, or Skill Normal Distributions Key Standards addressed in this Lesson: MM3D2 Time allotted for this Lesson: Standard: MM3D2 Students will solve
More informationFrancine s bone density is 1.45 standard deviations below the mean hip bone density for 25-year-old women of 956 grams/cm 2.
Chapter 3 Solutions 3.1 3.2 3.3 87% of the girls her daughter s age weigh the same or less than she does and 67% of girls her daughter s age are her height or shorter. According to the Los Angeles Times,
More informationACMS Statistics for Life Sciences. Chapter 9: Introducing Probability
ACMS 20340 Statistics for Life Sciences Chapter 9: Introducing Probability Why Consider Probability? We re doing statistics here. Why should we bother with probability? As we will see, probability plays
More informationLecture 6. Probability events. Definition 1. The sample space, S, of a. probability experiment is the collection of all
Lecture 6 1 Lecture 6 Probability events Definition 1. The sample space, S, of a probability experiment is the collection of all possible outcomes of an experiment. One such outcome is called a simple
More informationProperties of Continuous Probability Distributions The graph of a continuous probability distribution is a curve. Probability is represented by area
Properties of Continuous Probability Distributions The graph of a continuous probability distribution is a curve. Probability is represented by area under the curve. The curve is called the probability
More informationContinuous RVs. 1. Suppose a random variable X has the following probability density function: π, zero otherwise. f ( x ) = sin x, 0 < x < 2
STAT 4 Exam I Continuous RVs Fall 7 Practice. Suppose a random variable X has the following probability density function: f ( x ) = sin x, < x < π, zero otherwise. a) Find P ( X < 4 π ). b) Find µ = E
More information(i) The mean and mode both equal the median; that is, the average value and the most likely value are both in the middle of the distribution.
MATH 382 Normal Distributions Dr. Neal, WKU Measurements that are normally distributed can be described in terms of their mean µ and standard deviation σ. These measurements should have the following properties:
More informationLecture 4B: Chapter 4, Section 4 Quantitative Variables (Normal)
Lecture 4B: Chapter 4, Section 4 Quantitative Variables (Normal) Quantitative Sample vs. Population 68-95-99.7 Rule for Normal Curve Standardizing to z-scores Unstandardizing Cengage Learning Elementary
More informationBusiness Statistics: A Decision-Making Approach, 6e. Chapter Goals
Chapter 4 Student Lecture Notes 4-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter 4 Using Probability and Probability Distributions Fundamentals of Business Statistics Murali Shanker
More informationStatistics Lecture 3
Statistics 111 - Lecture 3 Continuous Random Variables The probable is what usually happens. (Aristotle ) Moore, McCabe and Craig: Section 4.3,4.5 Continuous Random Variables Continuous random variables
More informationChapter 4 - Lecture 3 The Normal Distribution
Chapter 4 - Lecture 3 The October 28th, 2009 Chapter 4 - Lecture 3 The Standard Chapter 4 - Lecture 3 The Standard Normal distribution is a statistical unicorn It is the most important distribution in
More informationFENG CHIA UNIVERSITY
FENG CHIA UNIVERSITY Fundamentals of Physics I (With Lab) PHYS114, Summer 2018 (May14-Jun15) Lecturer: TBA E-mail: TBA Time: Monday through Friday Contact hours: 60 (50 minutes each) Credits: 4 Office
More informationWhat does a population that is normally distributed look like? = 80 and = 10
What does a population that is normally distributed look like? = 80 and = 10 50 60 70 80 90 100 110 X Empirical Rule 68% 95% 99.7% 68-95-99.7% RULE Empirical Rule restated 68% of the data values fall within
More informationObjective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode.
Chapter 3 Numerically Summarizing Data Chapter 3.1 Measures of Central Tendency Objective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode. A1. Mean The
More information6/25/14. The Distribution Normality. Bell Curve. Normal Distribution. Data can be "distributed" (spread out) in different ways.
The Distribution Normality Unit 6 Sampling and Inference 6/25/14 Algebra 1 Ins2tute 1 6/25/14 Algebra 1 Ins2tute 2 MAFS.912.S-ID.1: Summarize, represent, and interpret data on a single count or measurement
More informationProbability Distribution for a normal random variable x:
Chapter5 Continuous Random Variables 5.3 The Normal Distribution Probability Distribution for a normal random variable x: 1. It is and about its mean µ. 2. (the that x falls in the interval a < x < b is
More informationHomework 4 Solutions Math 150
Homework Solutions Math 150 Enrique Treviño 3.2: (a) The table gives P (Z 1.13) = 0.1292. P (Z > 1.13) = 1 0.1292 = 0.8708. The table yields P (Z 0.18) = 0.571. (c) The table doesn t consider Z > 8 but
More informationLecture 10/Chapter 8 Bell-Shaped Curves & Other Shapes. From a Histogram to a Frequency Curve Standard Score Using Normal Table Empirical Rule
Lecture 10/Chapter 8 Bell-Shaped Curves & Other Shapes From a Histogram to a Frequency Curve Standard Score Using Normal Table Empirical Rule From Histogram to Normal Curve Start: sample of female hts
More informationEQ: What is a normal distribution?
Unit 5 - Statistics What is the purpose EQ: What tools do we have to assess data? this unit? What vocab will I need? Vocabulary: normal distribution, standard, nonstandard, interquartile range, population
More informationStochastic calculus for summable processes 1
Stochastic calculus for summable processes 1 Lecture I Definition 1. Statistics is the science of collecting, organizing, summarizing and analyzing the information in order to draw conclusions. It is a
More information2.1 The Rectangular Coordinate System
. The Rectangular Coordinate Sstem In this section ou will learn to: plot points in a rectangular coordinate sstem understand basic functions of the graphing calculator graph equations b generating a table
More informationContinuous Random Variables
Continuous Random Variables MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2018 Objectives During this lesson we will learn to: use the uniform probability distribution,
More information8.1 Frequency Distribution, Frequency Polygon, Histogram page 326
page 35 8 Statistics are around us both seen and in ways that affect our lives without us knowing it. We have seen data organized into charts in magazines, books and newspapers. That s descriptive statistics!
More informationSection 5.4. Ken Ueda
Section 5.4 Ken Ueda Students seem to think that being graded on a curve is a positive thing. I took lasers 101 at Cornell and got a 92 on the exam. The average was a 93. I ended up with a C on the test.
More informationMath 389: Advanced Analysis First Lecture
Math 389: Advanced Analysis First Lecture Steven J Miller Williams College sjm1@williams.edu http://www.williams.edu/mathematics/sjmiller/public_html/317 Bronfman B34 Williams College, September 5, 2014
More informationDifference Between Pair Differences v. 2 Samples
1 Sectio1.1 Comparing Two Proportions Learning Objectives After this section, you should be able to DETERMINE whether the conditions for performing inference are met. CONSTRUCT and INTERPRET a confidence
More informationChapter 6: SAMPLING DISTRIBUTIONS
Chapter 6: SAMPLING DISTRIBUTIONS Read Section 1.5 Graphical methods may not always be sufficient for describing data. Numerical measures can be created for both populations and samples. Definition A numerical
More informationECO220Y Continuous Probability Distributions: Uniform and Triangle Readings: Chapter 9, sections
ECO220Y Continuous Probability Distributions: Uniform and Triangle Readings: Chapter 9, sections 9.8-9.9 Fall 2011 Lecture 8 Part 1 (Fall 2011) Probability Distributions Lecture 8 Part 1 1 / 19 Probability
More informationData Analysis and Statistical Methods Statistics 651
Data Analysis and Statistical Methods Statistics 651 http://www.stat.tamu.edu/~suhasini/teaching.html Suhasini Subba Rao Review Our objective: to make confident statements about a parameter (aspect) in
More informationLearning Plan 09. Question 1. Question 2. Question 3. Question 4. What is the difference between the highest and lowest data values in a data set?
Learning Plan 09 Question 1 What is the difference between the highest and lowest data values in a data set? The difference is called range. (p. 794) Question 2 Measures of Dispersion. Read the answer
More informationBusiness Statistics. Chapter 6 Review of Normal Probability Distribution QMIS 220. Dr. Mohammad Zainal
Department of Quantitative Methods & Information Systems Business Statistics Chapter 6 Review of Normal Probability Distribution QMIS 220 Dr. Mohammad Zainal Chapter Goals After completing this chapter,
More informationThe Normal Distribution
Chapter 7 The Normal Distribution Section 7-1 Continuous Random Variables and Density Functions Recall the definitions Let S be the sample space of a probability experiment. A random variable X is a function
More informationStat 400 section 4.1 Continuous Random Variables
Stat 400 section 4. Continuous Random Variables notes by Tim Pilachowski Suppose we measure the heights of 5 people to the nearest inch and get the following results: height (in.) 64 65 66 67 68 69 70
More information6A Lab Post-test. Instructions for printed version. Week 10, Fall 2016
6A Lab Post-test Instructions for printed version Week 10, Fall 2016 This is the printed version of 6A Lab post-test. Please complete it during your final 6A lab, which will occur during week 10. DO NOT
More information68% 95% 99.7% x x 1 σ. x 1 2σ. x 1 3σ. Find a normal probability
11.3 a.1, 2A.1.B TEKS Use Normal Distributions Before You interpreted probability distributions. Now You will study normal distributions. Why? So you can model animal populations, as in Example 3. Key
More informationPre-Lab 0.2 Reading: Measurement
Name Block Pre-Lab 0.2 Reading: Measurement section 1 Description and Measurement Before You Read Weight, height, and length are common measurements. List at least five things you can measure. What You
More informationChapter 6. The Standard Deviation as a Ruler and the Normal Model 1 /67
Chapter 6 The Standard Deviation as a Ruler and the Normal Model 1 /67 Homework Read Chpt 6 Complete Reading Notes Do P129 1, 3, 5, 7, 15, 17, 23, 27, 29, 31, 37, 39, 43 2 /67 Objective Students calculate
More informationAnnouncements. Topics: Homework: - sec0ons 1.2, 1.3, and 2.1 * Read these sec0ons and study solved examples in your textbook!
Announcements Topics: - sec0ons 1.2, 1.3, and 2.1 * Read these sec0ons and study solved examples in your textbook! Homework: - review lecture notes thoroughly - work on prac0ce problems from the textbook
More informationAlgebra: Chapter 3 Notes
Algebra Homework: Chapter 3 (Homework is listed by date assigned; homework is due the following class period) HW# Date In-Class Homework 16 F 2/21 Sections 3.1 and 3.2: Solving and Graphing One-Step Inequalities
More informationWebsite information: Summer Learning -
Course: Chemistry 11 Teacher Name: Ms. Krista Wood & Murray Bulgar Contact information: kwood@sd44.ca; mbulgar@sd44.ca Website information: Summer Learning - http://www.sd44.ca/school/summer/pages/default.aspx
More informationUnit 8: Exponential & Logarithmic Functions
Date Period Unit 8: Eponential & Logarithmic Functions DAY TOPIC ASSIGNMENT 1 8.1 Eponential Growth Pg 47 48 #1 15 odd; 6, 54, 55 8.1 Eponential Decay Pg 47 48 #16 all; 5 1 odd; 5, 7 4 all; 45 5 all 4
More informationContinuous Probability Distributions
Continuous Probability Distributions Called a Probability density function. The probability is interpreted as "area under the curve." 1) The random variable takes on an infinite # of values within a given
More informationCOMS 4771 Lecture Course overview 2. Maximum likelihood estimation (review of some statistics)
COMS 4771 Lecture 1 1. Course overview 2. Maximum likelihood estimation (review of some statistics) 1 / 24 Administrivia This course Topics http://www.satyenkale.com/coms4771/ 1. Supervised learning Core
More informationWill Landau. Feb 28, 2013
Iowa State University The F Feb 28, 2013 Iowa State University Feb 28, 2013 1 / 46 Outline The F The F Iowa State University Feb 28, 2013 2 / 46 The normal (Gaussian) distribution A random variable X is
More informationSection 7.1 Properties of the Normal Distribution
Section 7.1 Properties of the Normal Distribution In Chapter 6, talked about probability distributions. Coin flip problem: Difference of two spinners: The random variable x can only take on certain discrete
More information26. LECTURE 26. Objectives
6. LECTURE 6 Objectives I understand the idea behind the Method of Lagrange Multipliers. I can use the method of Lagrange Multipliers to maximize a multivariate function subject to a constraint. Suppose
More informationGUIDED NOTES 2.2 LINEAR EQUATIONS IN ONE VARIABLE
GUIDED NOTES 2.2 LINEAR EQUATIONS IN ONE VARIABLE LEARNING OBJECTIVES In this section, you will: Solve equations in one variable algebraically. Solve a rational equation. Find a linear equation. Given
More informationThe normal distribution
The normal distribution Patrick Breheny September 29 Patrick Breheny Biostatistical Methods I (BIOS 5710) 1/28 A common histogram shape The normal curve Standardization Location-scale families A histograms
More informationChapter. Probability
Chapter 3 Probability Section 3.1 Basic Concepts of Probability Section 3.1 Objectives Identify the sample space of a probability experiment Identify simple events Use the Fundamental Counting Principle
More informationMeasurement. Measurement in Chemistry. Measurement. Stating a Measurement. The Metric System (SI) Basic Chemistry. Chapter 2 Measurements
Chapter 2 Lecture Chapter 2 Measurements 2.1 Units of Measurement Fifth Edition Measurement You make a measurement every time you measure your height read your watch take your temperature weigh a cantaloupe
More informationCentral Limit Theorem the Meaning and the Usage
Cetral Limit Theorem the Meaig ad the Usage Covetio about otatio. N, We are usig otatio X is variable with mea ad stadard deviatio. i lieu of sayig that X is a ormal radom Assume a sample of measuremets
More informationGUIDED NOTES 5.6 RATIONAL FUNCTIONS
GUIDED NOTES 5.6 RATIONAL FUNCTIONS LEARNING OBJECTIVES In this section, you will: Use arrow notation. Solve applied problems involving rational functions. Find the domains of rational functions. Identify
More informationMolar Calculations - Lecture Notes for Chapter 6. Lecture Notes Chapter Introduction
Page 1 of 9 Page 2 of 9 Lecture Notes Chapter 6 1. Introduction a. The above equation describes the synthesis of water from hydrogen and oxygen. b. It is not balanced, however. c. Notice how the number
More informationTeaching Research Methods: Resources for HE Social Sciences Practitioners. Sampling
Sampling Session Objectives By the end of the session you will be able to: Explain what sampling means in research List the different sampling methods available Have had an introduction to confidence levels
More informationPrefixes. Metric and SI Prefixes. Learning Check. Metric Equalities. Equalities. Basic Chemistry. Chapter 2 Lecture
Chapter 2 Lecture Chapter 2 2.4 Prefixes and Equalities Measurements Learning Goal Use the numerical values of prefixes to write a metric equality. Fifth Edition Prefixes A prefix in front of a unit increases
More informationSTA 291 Lecture 16. Normal distributions: ( mean and SD ) use table or web page. The sampling distribution of and are both (approximately) normal
STA 291 Lecture 16 Normal distributions: ( mean and SD ) use table or web page. The sampling distribution of and are both (approximately) normal X STA 291 - Lecture 16 1 Sampling Distributions Sampling
More information81920 = 118k. is(are) true? I The domain of g( x) = (, 2) (2, )
) person's MI (body mass inde) varies directly as an individual's weight in pounds and inversely as the square of the individual's height in inches. person who weighs 8 pounds and is 64 inches tall has
More informationLecture Notes Chapter 6
Lecture Notes Chapter 6 1. Introduction a. The above equation describes the synthesis of water from hydrogen and oxygen. b. It is not balanced, however. à c. Notice how the number of oxygen atoms on left
More information15 Discrete Distributions
Lecture Note 6 Special Distributions (Discrete and Continuous) MIT 4.30 Spring 006 Herman Bennett 5 Discrete Distributions We have already seen the binomial distribution and the uniform distribution. 5.
More informationKNES Primary School Year 5 Science Course Outline:
KNES Primary School Year 5 Science Course Outline: 2017-2018 Year Overview. The Year 5 program of study for Science will take students on a scientific adventure through various activities which will be
More informationLecture # 31. Questions of Marks 3. Question: Solution:
Lecture # 31 Given XY = 400, X = 5, Y = 4, S = 4, S = 3, n = 15. Compute the coefficient of correlation between XX and YY. r =0.55 X Y Determine whether two variables XX and YY are correlated or uncorrelated
More information10.1. Comparing Two Proportions. Section 10.1
/6/04 0. Comparing Two Proportions Sectio0. Comparing Two Proportions After this section, you should be able to DETERMINE whether the conditions for performing inference are met. CONSTRUCT and INTERPRET
More information6 THE NORMAL DISTRIBUTION
CHAPTER 6 THE NORMAL DISTRIBUTION 341 6 THE NORMAL DISTRIBUTION Figure 6.1 If you ask enough people about their shoe size, you will find that your graphed data is shaped like a bell curve and can be described
More informationTRAINING LAB BLOOD AS EVIDENCE ANALYZING BLOOD SPATTER NAME
TRAINING LAB BLOOD AS EVIDENCE ANALYZING BLOOD SPATTER NAME Background: You have learned how to analyze individual blood drops to determine the height a passive drop fell, the direction a moving drop was
More informationChapter 10: Comparing Two Populations or Groups
Chapter 10: Comparing Two Populations or Groups Sectio0.1 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 10 Comparing Two Populations or Groups 10.1 10.2 Comparing Two Means
More informationElementary Statistics
Elementary Statistics Q: What is data? Q: What does the data look like? Q: What conclusions can we draw from the data? Q: Where is the middle of the data? Q: Why is the spread of the data important? Q:
More informationChapter 5. Means and Variances
1 Chapter 5 Means and Variances Our discussion of probability has taken us from a simple classical view of counting successes relative to total outcomes and has brought us to the idea of a probability
More informationChapter 10: Comparing Two Populations or Groups
Chapter 10: Comparing Two Populations or Groups Sectio0.1 The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 10 Comparing Two Populations or Groups 10.1 10. Comparing Two Means
More informationPELLISSIPPI STATE COMMUNITY COLLEGE MASTER SYLLABUS NONCALCULUS BASED PHYSICS I PHYS 2010
PELLISSIPPI STATE COMMUNITY COLLEGE MASTER SYLLABUS NONCALCULUS BASED PHYSICS I PHYS 2010 Class Hours: 3.0 Credit Hours: 4.0 Laboratory Hours: 3.0 Revised: Spring 2011 Catalog Course Description: This
More informationCompounds Worksheet Answer Key
9.2 Naming And Writing Formulas For Ionic Compounds Worksheet Answer Key through practice problems in naming and writing formulas of ionic. Naming Ionic Compounds Practice Worksheet. (UPDATED): and formula.
More informationChapter 7: Theoretical Probability Distributions Variable - Measured/Categorized characteristic
BSTT523: Pagano & Gavreau, Chapter 7 1 Chapter 7: Theoretical Probability Distributions Variable - Measured/Categorized characteristic Random Variable (R.V.) X Assumes values (x) by chance Discrete R.V.
More informationLinear Relations and Functions
Linear Relations and Functions Why? You analyzed relations and functions. (Lesson 2-1) Now Identify linear relations and functions. Write linear equations in standard form. New Vocabulary linear relations
More informationZero and Negative Exponents
0.4 Zero and Negative Exponents How can you evaluate a nonzero number with an exponent of zero? How can you evaluate a nonzero number with a negative integer exponent? ACTIVITY: Using the Quotient of Powers
More informationPrerequisites: CHEM 1312 and CHEM 1112, or CHEM 1412 General Chemistry II (Lecture and Laboratory)
Course Syllabus CHEM 2423 Organic Chemistry I Revision Date: 8/19/2013 Catalog Description: Fundamental principles of organic chemistry will be studied, including the structure, bonding, properties, and
More informationMath 105 Course Outline
Math 105 Course Outline Week 9 Overview This week we give a very brief introduction to random variables and probability theory. Most observable phenomena have at least some element of randomness associated
More informationLecture #16 Thursday, October 13, 2016 Textbook: Sections 9.3, 9.4, 10.1, 10.2
STATISTICS 200 Lecture #16 Thursday, October 13, 2016 Textbook: Sections 9.3, 9.4, 10.1, 10.2 Objectives: Define standard error, relate it to both standard deviation and sampling distribution ideas. Describe
More informationChapter 3. Exponential and Logarithmic Functions. 3.2 Logarithmic Functions
Chapter 3 Exponential and Logarithmic Functions 3.2 Logarithmic Functions 1/23 Chapter 3 Exponential and Logarithmic Functions 3.2 4, 8, 14, 16, 18, 20, 22, 30, 31, 32, 33, 34, 39, 42, 54, 56, 62, 68,
More informationWelcome to Physics 211! General Physics I
Welcome to Physics 211! General Physics I Physics 211 Fall 2015 Lecture 01-1 1 Physics 215 Honors & Majors Are you interested in becoming a physics major? Do you have a strong background in physics and
More informationBe prepared to find the volume, area, and volume of any of the shapes covered in lecture and/or homework. A rhombus is also a square.
Math 254SI Practice Problem Set 5 (Chapter 8&9) Do these problems on a separate piece of paper(s). Remember that the quiz is closed book and closed notes except for the Geometry handout that I will provide.
More information6.1 Using Properties of Exponents 1. Use properties of exponents to evaluate and simplify expressions involving powers. Product of Powers Property
6.1 Using Properties of Exponents Objectives 1. Use properties of exponents to evaluate and simplify expressions involving powers. 2. Use exponents and scientific notation to solve real life problems.
More information