8.8 APPLICATIONS OF THE NORMAL CURVE

Size: px
Start display at page:

Download "8.8 APPLICATIONS OF THE NORMAL CURVE"

Transcription

1 8.8 APPLICATIONS OF THE NORMAL CURVE If a set of real data, such as test scores or weights of persons or things, can be assumed to be generated by a normal probability model, the table of standard normal-curve areas can be applied to solve the problem even when the data are not standard normal by standardiing the quantities involved in the problem. Example 8.5 The lifetime of a certain type of battery has been found to be normally distributed with a mean of 200 hours and a standard deviation of 15 hours (this sort of information could be gathered, for example, by keeping records at the factory on the lifetimes of samples of batteries over a long period of time). What proportion of these batteries can be expected to last less than 220 hours? Probabilities can be thought of as proportions, so this is a probability problem. The assumed distribution of battery lifetimes is shown in Figure The shaded region shows the batteries that have a lifetime of less than 220 hours. We can calculate this area using the table of normal-curve areas if we know the -statistic value corresponding to 220 hours Thus p(lifetime 220) p( 1. 33), where 1.33 is 220 standardied.

2 Hours Figure 8.20 p(battery life 220 hours). We now know the value of that corresponds to 220 hours. Using this value, we can get the area of the shaded region in Figure 8.20 from the table of normal-curve areas (again, assuming that the battery lives are generated by a normal probability model). That is, we can find p ( 1. 33) From the table, we find the area to be , so the proportion of batteries with lifetimes shorter than 220 hours (which corresponds to a of 1.33) is expected to be 0.91 (rounded). That is, about 91% of the batteries can be expected to last less than 220 hours. Example 8.6 What proportion of the batteries from Example 8.5 can be expected to last more than 220 hours? Again, assuming the battery lifetimes to be distributed normally, we have the graph shown in Figure The shaded region represents the proportion of batteries with lifetimes greater than 220 hours. Since the corresponding to 220 hours is 1.33, we want to find p ( 1. 33) We know from the table that p ( 1. 33) 0. 91

3 Hours Figure 8.21 p(battery life 220 hours). Once again we use the fact that p(event) 1 p(complement of the event). So p ( 1. 33) We expect about 0.09 (or 9%) of the batteries to last more than 220 hours. Example 8.7 The SPWEHIQS Club (Society of People with Extremely High IQs) requires people to take an intelligence test as a condition for joining the club and restricts membership to the top 5% as measured by this test. Suppose the scores on the intelligence test have a mean of 100 and a standard deviation of 12 and are normally distributed for very large groups of people. What is the lowest score on this test that would be acceptable for admission to SPWEHIQS? Figure 8.22 shows the distribution of the scores of the intelligence test. The figure indicates that 5%, or a proportion of 0.05, of the total area is in the shaded region under the curve. According to the normal-curve table (Table E), this area corresponds to a statistic of A statistic here is computed as IQ Thus a statistic can be changed to an intelligence test score by a scaling factor of 12 (the standard deviation of the test scores) and a centering factor of 100 (the mean of the test scores). So the test score corresponding to a statistic (score) of 1.65 is IQ 12(1. 65)

4 Area = IQ = Figure 8.22 p (IQ?) Rounding this score to 120, we find that a score of 120 would be the lowest acceptable for admission to the club. Example 8.8 A certain insect species has a mean length of 1.2 centimeters and a standard deviation of 0.12 centimeters. If there are estimated to be 1000 of these insects in a terrarium, how many would be expected to be less than 1 centimeter in length? Assume that the lengths are normally distributed. Figure 8.23 is a sketch of the distribution of the insect lengths. The shaded part of the graph begins at the 1-centimeter mark and includes the region to the left of this point (since the problem specifies insects having lengths less than 1 centimeter). The statistic corresponding to 1 centimeter is found by the transformation According to Table E, the area to the left of is So a proportion of (4.75%) of the 1000 insects are expected to be less than 1 centimeter long. That is, we expect to be less than 1 centimeter in length insects

5 Area = Length = Figure 8.23 p(insect length 1 cm). SECTION 8.8 EXERCISES Suppose 30 million boxes of bananas are packed a year. Given this packing plant For each of the following problems, if the exact rule and the assumption about the distrivalue is not available in the table, use the closest bution of box weights upon arrival, how many one. boxes would be expected to weigh less than 1. The heights of a group of male students follow 40 pounds upon arrival? ( Note: Tables tell us the normal distribution with mean 70 inches that for a standard normal, p( 4. 00) and standard deviation 3.1 inches ) a. What percentage of the students would 3. A car manufacturer is producing a piston you expect to be shorter than 68 inches? for its engines. The piston is supposed to b. What percentage of the students would have a diameter of 5.3 inches, but because of you expect to be taller than 73.5 inches? variability, the diameter of a piston actually c. What height are 31% of the students follows a normal distribution with a mean of shorter than, and what height are 69% of 5.3 and a standard deviation of If a piston them taller than? is more than inch away from the needed 2. To help ensure that boxes of its bananas weigh sie of 5.3 inches, the piston is rejected. at least 40 pounds upon arrival at their destiexpect to be too large? a. What percentage of the pistons would you nation, a packing plant might adopt this rule: Pack boxes to have a weight of 41.5 pounds of b. What percentage of the pistons would you bananas with a maximum permissible range expect to be too small? Hint: Recall that a of 3 ounces above or below 41 pounds, 8 probability is converted to a percentage by ounces (that is, pack boxes to have at least moving the decimal point two places right. 41 pounds, 5 ounces, but no more than Recall the situation presented in Exercise 3. pounds, 11 ounces, of bananas). With this rule Suppose instead, because of a mechanical and the shrinkage in travel, the distribution of problem with the machine producing the pis- box weights upon arrival may be assumed to tons, the pistons have diameters that follow be approximately normal with a mean of 41 a normal distribution with a mean of 5.29 pounds and a standard deviation of 4 ounces. inches. The standard deviation is still 0.01.

6 The specifications require the diameter of the piston to be 5.3 plus or minus a. What percentage of the pistons would you expect to be too large in this situation? b. What percentage of the pistons would you expect to be too small? 5. A set of final exam scores has a mean of 52 and a standard deviation of 6. The scores are normally distributed. If a teacher wants to assign a grade of A to the top 15% of the scores, what score should be the lowest A? If the bottom 15% are to be Fs, what test score should be the highest F? 6. A pipette is a precise instrument used in science to dispense an exact amount of liquid. The pipette is carefully calibrated, but, as with any measurement, it will not dispense the same amount each time. The error in amount is well described by the normal distribution. Suppose a scientist is using a pipette known to dispense amounts with a standard deviation of 0.05 microliter (a microliter is a millionth of a liter). The scientist is able to set the pipette to dispense varying amounts of liquid. a. If the pipette is set to dispense 200 microliters, what percentage of the time will it dispense greater than microliters? b. If the pipette is set to dispense 175 mi- croliters, what percentage of the time will it dispense less than microliters of liquid? c. The scientist wanted to set the pipette to dispense 200 microliters, but she acciden- tally set it to 199. Is there any chance that the pipette will dispense as much as 200 microliters? For additional exercises, see page 727.

6.3 Applications of Normal Distributions

6.3 Applications of Normal Distributions 6.3 Applications of Normal Distributions Objectives: 1. Find probabilities and percentages from known values. 2. Find values from known areas. Overview: This section presents methods for working with normal

More information

The Normal Distribution

The Normal Distribution Chapter 6 The Normal Distribution 6.1 The Normal Distribution 1 6.1.1 Student Learning Objectives By the end of this chapter, the student should be able to: Recognize the normal probability distribution

More information

Section 1.3 Exercises (Solutions)

Section 1.3 Exercises (Solutions) Section 1.3 Exercises (s) 1.109, 1.110, 1.111, 1.114*, 1.115, 1.119*, 1.122, 1.125, 1.127*, 1.128*, 1.131*, 1.133*, 1.135*, 1.137*, 1.139*, 1.145*, 1.146-148. 1.109 Sketch some normal curves. (a) Sketch

More information

Unit 8: Normal Calculations

Unit 8: Normal Calculations Unit 8: Normal Calculations Summary of Video In this video, we continue the discussion of normal curves that was begun in Unit 7. Recall that a normal curve is bell-shaped and completely characterized

More information

1) What is the probability that the random variable has a value greater than 2? A) 0.750 B) 0.625 C) 0.875 D) 0.700

1) What is the probability that the random variable has a value greater than 2? A) 0.750 B) 0.625 C) 0.875 D) 0.700 Practice for Chapter 6 & 7 Math 227 This is merely an aid to help you study. The actual exam is not multiple choice nor is it limited to these types of questions. Using the following uniform density curve,

More information

Unit 7: Normal Curves

Unit 7: Normal Curves Unit 7: Normal Curves Summary of Video Histograms of completely unrelated data often exhibit similar shapes. To focus on the overall shape of a distribution and to avoid being distracted by the irregularities

More information

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

Density Curve. A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: Density Curve A density curve is the graph of a continuous probability distribution. It must satisfy the following properties: 1. The total area under the curve must equal 1. 2. Every point on the curve

More information

MATH FOR NURSING MEASUREMENTS. Written by: Joe Witkowski and Eileen Phillips

MATH FOR NURSING MEASUREMENTS. Written by: Joe Witkowski and Eileen Phillips MATH FOR NURSING MEASUREMENTS Written by: Joe Witkowski and Eileen Phillips Section 1: Introduction Quantities have many units, which can be used to measure them. The following table gives common units

More information

Lesson 20. Probability and Cumulative Distribution Functions

Lesson 20. Probability and Cumulative Distribution Functions Lesson 20 Probability and Cumulative Distribution Functions Recall If p(x) is a density function for some characteristic of a population, then Recall If p(x) is a density function for some characteristic

More information

Mass and Volume Relationships

Mass and Volume Relationships Mass and Volume Relationships Objective: The purpose of this laboratory exercise is to become familiar with some of the basic relationships and units used by scientists. In this experiment you will perform

More information

Chapter 8 Homework ( ) -- Normal Distribution

Chapter 8 Homework ( ) -- Normal Distribution Chapter 8 Homework (195-198) -- Normal Distribution Dr. McGahagan NOTE: I often abbreviate the text declaration that X is a random variable distributed normally with mean 8 and variance of 144 as " X is

More information

Complement: 0.4 x 0.8 = =.6

Complement: 0.4 x 0.8 = =.6 Homework Chapter 5 Name: 1. Use the graph below 1 a) Why is the total area under this curve equal to 1? Rectangle; A = LW A = 1(1) = 1 b) What percent of the observations lie above 0.8? 1 -.8 =.2; A =

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. STATISTICS/GRACEY PRACTICE TEST/EXAM 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the given random variable as being discrete or continuous.

More information

18) 6 3 4 21) 1 1 2 22) 7 1 2 23) 19 1 2 25) 1 1 4. 27) 6 3 qt to cups 30) 5 1 2. 32) 3 5 gal to pints. 33) 24 1 qt to cups

18) 6 3 4 21) 1 1 2 22) 7 1 2 23) 19 1 2 25) 1 1 4. 27) 6 3 qt to cups 30) 5 1 2. 32) 3 5 gal to pints. 33) 24 1 qt to cups Math 081 Chapter 07 Practice Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 18) 6 3 4 gal to quarts Convert as indicated. 1) 72 in. to feet 19)

More information

Grade 12 Consumer Mathematics Standards Test. Written Test Student Booklet

Grade 12 Consumer Mathematics Standards Test. Written Test Student Booklet Grade 12 Consumer Mathematics Standards Test Written Test Student Booklet January 2011 Manitoba Education Cataloguing in Publication Data Grade 12 Consumer Mathematics Standards Test : Written Test Student

More information

Math 140 (4,5,6) Sample Exam II Fall 2011

Math 140 (4,5,6) Sample Exam II Fall 2011 Math 140 (4,5,6) Sample Exam II Fall 2011 Provide an appropriate response. 1) In a sample of 10 randomly selected employees, it was found that their mean height was 63.4 inches. From previous studies,

More information

7. Normal Distributions

7. Normal Distributions 7. Normal Distributions A. Introduction B. History C. Areas of Normal Distributions D. Standard Normal E. Exercises Most of the statistical analyses presented in this book are based on the bell-shaped

More information

Def: The standard normal distribution is a normal probability distribution that has a mean of 0 and a standard deviation of 1.

Def: The standard normal distribution is a normal probability distribution that has a mean of 0 and a standard deviation of 1. Lecture 6: Chapter 6: Normal Probability Distributions A normal distribution is a continuous probability distribution for a random variable x. The graph of a normal distribution is called the normal curve.

More information

Exercises - The Normal Curve

Exercises - The Normal Curve Exercises - The Normal Curve 1. Find e following proportions under e Normal curve: a) P(z>2.05) b) P(z>2.5) c) P(-1.25

More information

AP Statistics Solutions to Packet 2

AP Statistics Solutions to Packet 2 AP Statistics Solutions to Packet 2 The Normal Distributions Density Curves and the Normal Distribution Standard Normal Calculations HW #9 1, 2, 4, 6-8 2.1 DENSITY CURVES (a) Sketch a density curve that

More information

Mind on Statistics. Chapter 8

Mind on Statistics. Chapter 8 Mind on Statistics Chapter 8 Sections 8.1-8.2 Questions 1 to 4: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. 1. Random variable

More information

Keystone National Middle School Math Level 7 Placement Exam

Keystone National Middle School Math Level 7 Placement Exam Keystone National Middle School Math Level 7 Placement Exam ) Erica bought a car for $,000. She had to add Pennsylvania s sales tax of 6%. The total price of the car is closest to? $,00 $6,000 $,000 $,000

More information

13.2 Measures of Central Tendency

13.2 Measures of Central Tendency 13.2 Measures of Central Tendency Measures of Central Tendency For a given set of numbers, it may be desirable to have a single number to serve as a kind of representative value around which all the numbers

More information

DIMENSIONAL ANALYSIS #2

DIMENSIONAL ANALYSIS #2 DIMENSIONAL ANALYSIS #2 Area is measured in square units, such as square feet or square centimeters. These units can be abbreviated as ft 2 (square feet) and cm 2 (square centimeters). For example, we

More information

Student Exploration: Unit Conversions

Student Exploration: Unit Conversions Name: Date: Student Exploration: Unit Conversions Vocabulary: base unit, cancel, conversion factor, dimensional analysis, metric system, prefix, scientific notation Prior Knowledge Questions (Do these

More information

Key Concept. Density Curve

Key Concept. Density Curve MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 6 Normal Probability Distributions 6 1 Review and Preview 6 2 The Standard Normal Distribution 6 3 Applications of Normal

More information

Biological Principles Lab: Scientific Measurements

Biological Principles Lab: Scientific Measurements Biological Principles Lab: Scientific Measurements Name: PURPOSE To become familiar with the reference units and prefixes in the metric system. To become familiar with some common laboratory equipment.

More information

The Normal Distribution

The Normal Distribution The Normal Distribution Continuous Distributions A continuous random variable is a variable whose possible values form some interval of numbers. Typically, a continuous variable involves a measurement

More information

Converting Units of Measure Measurement

Converting Units of Measure Measurement Converting Units of Measure Measurement Outcome (lesson objective) Given a unit of measurement, students will be able to convert it to other units of measurement and will be able to use it to solve contextual

More information

8 th Grade Task 2 Rugs

8 th Grade Task 2 Rugs 8 th Grade Task 2 Rugs Student Task Core Idea 4 Geometry and Measurement Find perimeters of shapes. Use Pythagorean theorem to find side lengths. Apply appropriate techniques, tools and formulas to determine

More information

MEASUREMENT. Historical records indicate that the first units of length were based on people s hands, feet and arms. The measurements were:

MEASUREMENT. Historical records indicate that the first units of length were based on people s hands, feet and arms. The measurements were: MEASUREMENT Introduction: People created systems of measurement to address practical problems such as finding the distance between two places, finding the length, width or height of a building, finding

More information

Chapter 3 Normal Distribution

Chapter 3 Normal Distribution Chapter 3 Normal Distribution Density curve A density curve is an idealized histogram, a mathematical model; the curve tells you what values the quantity can take and how likely they are. Example Height

More information

DIMENSIONAL ANALYSIS #2

DIMENSIONAL ANALYSIS #2 DIMENSIONAL ANALYSIS #2 Area is measured in square units, such as square feet or square centimeters. These units can be abbreviated as ft 2 (square feet) and cm 2 (square centimeters). For example, we

More information

5.4 Solving Percent Problems Using the Percent Equation

5.4 Solving Percent Problems Using the Percent Equation 5. Solving Percent Problems Using the Percent Equation In this section we will develop and use a more algebraic equation approach to solving percent equations. Recall the percent proportion from the last

More information

Basic Statistics Self Assessment Test

Basic Statistics Self Assessment Test Basic Statistics Self Assessment Test Professor Douglas H. Jones PAGE 1 A soda-dispensing machine fills 12-ounce cans of soda using a normal distribution with a mean of 12.1 ounces and a standard deviation

More information

CHAPTER 6: Continuous Uniform Distribution: 6.1. Definition: The density function of the continuous random variable X on the interval [A, B] is.

CHAPTER 6: Continuous Uniform Distribution: 6.1. Definition: The density function of the continuous random variable X on the interval [A, B] is. Some Continuous Probability Distributions CHAPTER 6: Continuous Uniform Distribution: 6. Definition: The density function of the continuous random variable X on the interval [A, B] is B A A x B f(x; A,

More information

Mathematics Common Core Sample Questions

Mathematics Common Core Sample Questions New York State Testing Program Mathematics Common Core Sample Questions Grade5 The materials contained herein are intended for use by New York State teachers. Permission is hereby granted to teachers and

More information

6.4 Normal Distribution

6.4 Normal Distribution Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under

More information

12 Hypothesis Testing

12 Hypothesis Testing CHAPTER 12 Hypothesis Testing Chapter Outline 12.1 HYPOTHESIS TESTING 12.2 CRITICAL VALUES 12.3 ONE-SAMPLE T TEST 247 12.1. Hypothesis Testing www.ck12.org 12.1 Hypothesis Testing Learning Objectives Develop

More information

Quarterly Cumulative Test 2

Quarterly Cumulative Test 2 Select the best answer. 1. Find the difference 90 37.23. A 67.23 C 52.77 B 57.77 D 32.23 2. Which ratio is equivalent to 3 20? F 5 to 100 H 140 to 21 G 100 to 5 J 21 to 140 3. Alonda purchased 8 for $2.00.

More information

Chapter 1 Lecture Notes: Science and Measurements

Chapter 1 Lecture Notes: Science and Measurements Educational Goals Chapter 1 Lecture Notes: Science and Measurements 1. Explain, compare, and contrast the terms scientific method, hypothesis, and experiment. 2. Compare and contrast scientific theory

More information

What Makes a Good Resource Data Handling Murder Investigation

What Makes a Good Resource Data Handling Murder Investigation A Murder Investigation A professional murder has taken place. It is believed that the victim was poisoned before being shot. The murderer is one of ten known villains as seen below. You are to use the

More information

Chapter 5: The normal approximation for data

Chapter 5: The normal approximation for data Chapter 5: The normal approximation for data Context................................................................... 2 Normal curve 3 Normal curve.............................................................

More information

Fractions, decimals and percentages

Fractions, decimals and percentages Fractions, decimals and percentages Some notes for the lesson. Extra practice questions available. A. Quick quiz on units Some of the exam questions will have units in them, and you may have to convert

More information

SHELL INDUSTRIAL APTITUDE BATTERY PREPARATION GUIDE

SHELL INDUSTRIAL APTITUDE BATTERY PREPARATION GUIDE SHELL INDUSTRIAL APTITUDE BATTERY PREPARATION GUIDE 2011 Valtera Corporation. All rights reserved. TABLE OF CONTENTS OPERATIONS AND MAINTENANCE JOB REQUIREMENTS... 1 TEST PREPARATION... 2 USE OF INDUSTRIAL

More information

Statistical Inference

Statistical Inference Statistical Inference Idea: Estimate parameters of the population distribution using data. How: Use the sampling distribution of sample statistics and methods based on what would happen if we used this

More information

Answer: The two quantities are equal 1. An equilateral triangle has equal side lengths, so the ratio is always going to be 1:1.

Answer: The two quantities are equal 1. An equilateral triangle has equal side lengths, so the ratio is always going to be 1:1. Question Test 2, Second QR Section (version ) The length of each side of equilateral triangle T is... QA: Ratio of one side of T to another side of T QB: Ratio of one side of X to another side of X Geometry:

More information

AP Statistics Semester Exam Review Chapters 1-3

AP Statistics Semester Exam Review Chapters 1-3 AP Statistics Semester Exam Review Chapters 1-3 1. Here are the IQ test scores of 10 randomly chosen fifth-grade students: 145 139 126 122 125 130 96 110 118 118 To make a stemplot of these scores, you

More information

Algebra 1: Basic Skills Packet Page 1 Name: Integers 1. 54 + 35 2. 18 ( 30) 3. 15 ( 4) 4. 623 432 5. 8 23 6. 882 14

Algebra 1: Basic Skills Packet Page 1 Name: Integers 1. 54 + 35 2. 18 ( 30) 3. 15 ( 4) 4. 623 432 5. 8 23 6. 882 14 Algebra 1: Basic Skills Packet Page 1 Name: Number Sense: Add, Subtract, Multiply or Divide without a Calculator Integers 1. 54 + 35 2. 18 ( 30) 3. 15 ( 4) 4. 623 432 5. 8 23 6. 882 14 Decimals 7. 43.21

More information

6 3 The Standard Normal Distribution

6 3 The Standard Normal Distribution 290 Chapter 6 The Normal Distribution Figure 6 5 Areas Under a Normal Distribution Curve 34.13% 34.13% 2.28% 13.59% 13.59% 2.28% 3 2 1 + 1 + 2 + 3 About 68% About 95% About 99.7% 6 3 The Distribution Since

More information

Unit 26 Estimation with Confidence Intervals

Unit 26 Estimation with Confidence Intervals Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Sample Final Exam Spring 2008 DeMaio Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given degree of confidence and sample data to construct

More information

Characteristics of the Four Main Geometrical Figures

Characteristics of the Four Main Geometrical Figures Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.

More information

Title: Basic Medical Conversion Formulas

Title: Basic Medical Conversion Formulas Stackable Cert. Documentation Technology Study / Life skills EL-Civics Career Pathways Police Paramedic Fire Rescue Medical Asst. EKG / Cardio Phlebotomy Practical Nursing Healthcare Admin Pharmacy Tech

More information

Perfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through

Perfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through Perfume Packaging Gina would like to package her newest fragrance, Persuasive, in an eyecatching yet cost-efficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters

More information

Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area of Parallelograms, Triangles, and Trapezoids (pages 314 318) Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base

More information

NAME OF SCHOOL. Maths Literacy Grade 11. Paper 1

NAME OF SCHOOL. Maths Literacy Grade 11. Paper 1 NAME OF SCHOOL Maths Literacy Grade 11 Paper 1 2,5 hours 100 marks INSTRUCTIONS AND INFORMATION Read the following carefully before answering the questions: 1. Number the answers exactly as the questions

More information

Objective To introduce a formula to calculate the area. Family Letters. Assessment Management

Objective To introduce a formula to calculate the area. Family Letters. Assessment Management Area of a Circle Objective To introduce a formula to calculate the area of a circle. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

More information

EXAM #1 (Example) Instructor: Ela Jackiewicz. Relax and good luck!

EXAM #1 (Example) Instructor: Ela Jackiewicz. Relax and good luck! STP 231 EXAM #1 (Example) Instructor: Ela Jackiewicz Honor Statement: I have neither given nor received information regarding this exam, and I will not do so until all exams have been graded and returned.

More information

Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points. 2) 15% compounded semiannually

Find the effective rate corresponding to the given nominal rate. Round results to the nearest 0.01 percentage points. 2) 15% compounded semiannually Exam Name Find the compound amount for the deposit. Round to the nearest cent. 1) $1200 at 4% compounded quarterly for 5 years Find the effective rate corresponding to the given nominal rate. Round results

More information

Quick Reference ebook

Quick Reference ebook This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

More information

Thursday, November 13: 6.1 Discrete Random Variables

Thursday, November 13: 6.1 Discrete Random Variables Thursday, November 13: 6.1 Discrete Random Variables Read 347 350 What is a random variable? Give some examples. What is a probability distribution? What is a discrete random variable? Give some examples.

More information

AP * Statistics Review. Descriptive Statistics

AP * Statistics Review. Descriptive Statistics AP * Statistics Review Descriptive Statistics Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production

More information

Handout Unit Conversions (Dimensional Analysis)

Handout Unit Conversions (Dimensional Analysis) Handout Unit Conversions (Dimensional Analysis) The Metric System had its beginnings back in 670 by a mathematician called Gabriel Mouton. The modern version, (since 960) is correctly called "International

More information

Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.

Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square. Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional

More information

CHEM 101 / 105 LECT 1

CHEM 101 / 105 LECT 1 CHEM 101 / 105 LECT 1 Rules of the road: Your Loyola computer account (activate it). Class Web site (visit and send me an e-mail B4 Tues.) spavko1@luc.edu Chapter 1. Chemistry is... Matter is... Classifications

More information

Algebra I/Integrated I Released Form Calculator Active

Algebra I/Integrated I Released Form Calculator Active Algebra I/Integrated I Released Form Calculator Active 16. Which expression is equivalent to? 17. A school purchases boxes of candy bars. Each box contains 50 candy bars. Each box costs $30. How much does

More information

A Short Guide to Significant Figures

A Short Guide to Significant Figures A Short Guide to Significant Figures Quick Reference Section Here are the basic rules for significant figures - read the full text of this guide to gain a complete understanding of what these rules really

More information

Revision Notes Adult Numeracy Level 2

Revision Notes Adult Numeracy Level 2 Revision Notes Adult Numeracy Level 2 Place Value The use of place value from earlier levels applies but is extended to all sizes of numbers. The values of columns are: Millions Hundred thousands Ten thousands

More information

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication

FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby

More information

Task: Representing the National Debt 7 th grade

Task: Representing the National Debt 7 th grade Tennessee Department of Education Task: Representing the National Debt 7 th grade Rachel s economics class has been studying the national debt. The day her class discussed it, the national debt was $16,743,576,637,802.93.

More information

Test 4 Sample Problem Solutions, 27.58 = 27 47 100, 7 5, 1 6. 5 = 14 10 = 1.4. Moving the decimal two spots to the left gives

Test 4 Sample Problem Solutions, 27.58 = 27 47 100, 7 5, 1 6. 5 = 14 10 = 1.4. Moving the decimal two spots to the left gives Test 4 Sample Problem Solutions Convert from a decimal to a fraction: 0.023, 27.58, 0.777... For the first two we have 0.023 = 23 58, 27.58 = 27 1000 100. For the last, if we set x = 0.777..., then 10x

More information

Section 1 Tools and Measurement

Section 1 Tools and Measurement Section 1 Tools and Measurement Key Concept Scientists must select the appropriate tools to make measurements and collect data, to perform tests, and to analyze data. What You Will Learn Scientists use

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 0.4987 B) 0.9987 C) 0.0010 D) 0.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) 0.4987 B) 0.9987 C) 0.0010 D) 0. Ch. 5 Normal Probability Distributions 5.1 Introduction to Normal Distributions and the Standard Normal Distribution 1 Find Areas Under the Standard Normal Curve 1) Find the area under the standard normal

More information

Chapter 10 - Practice Problems 1

Chapter 10 - Practice Problems 1 Chapter 10 - Practice Problems 1 1. A researcher is interested in determining if one could predict the score on a statistics exam from the amount of time spent studying for the exam. In this study, the

More information

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B. Thursday, January 29, 2004 9:15 a.m. to 12:15 p.m.

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B. Thursday, January 29, 2004 9:15 a.m. to 12:15 p.m. The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS B Thursday, January 9, 004 9:15 a.m. to 1:15 p.m., only Print Your Name: Print Your School s Name: Print your name and

More information

The Math. P (x) = 5! = 1 2 3 4 5 = 120.

The Math. P (x) = 5! = 1 2 3 4 5 = 120. The Math Suppose there are n experiments, and the probability that someone gets the right answer on any given experiment is p. So in the first example above, n = 5 and p = 0.2. Let X be the number of correct

More information

1) The table lists the smoking habits of a group of college students. Answer: 0.218

1) The table lists the smoking habits of a group of college students. Answer: 0.218 FINAL EXAM REVIEW Name ) The table lists the smoking habits of a group of college students. Sex Non-smoker Regular Smoker Heavy Smoker Total Man 5 52 5 92 Woman 8 2 2 220 Total 22 2 If a student is chosen

More information

Section 2 Solving dosage problems

Section 2 Solving dosage problems Section 2 Solving dosage problems Whether your organization uses a bulk medication administration system or a unit-dose administration system to prepare to administer pediatric medications, you may find

More information

Measurement. Customary Units of Measure

Measurement. Customary Units of Measure Chapter 7 Measurement There are two main systems for measuring distance, weight, and liquid capacity. The United States and parts of the former British Empire use customary, or standard, units of measure.

More information

6.2 Normal distribution. Standard Normal Distribution:

6.2 Normal distribution. Standard Normal Distribution: 6.2 Normal distribution Slide Heights of Adult Men and Women Slide 2 Area= Mean = µ Standard Deviation = σ Donation: X ~ N(µ,σ 2 ) Standard Normal Distribution: Slide 3 Slide 4 a normal probability distribution

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

More information

Fractions and Decimals

Fractions and Decimals Fractions and Decimals Objectives To provide experience with renaming fractions as decimals and decimals as fractions; and to develop an understanding of the relationship between fractions and division.

More information

Summer Math Packet. For Students Entering Grade 5 $3.98. Student s Name 63 9 = Review and Practice of Fairfield Math Objectives and CMT Objectives

Summer Math Packet. For Students Entering Grade 5 $3.98. Student s Name 63 9 = Review and Practice of Fairfield Math Objectives and CMT Objectives Summer Math Packet 63 9 = Green Yellow Green Orange Orange Yellow $3.98 1 Green A B C D Red 8 1 2 3 4 5 Student s Name June 2013 Review and Practice of Fairfield Math Objectives and CMT Objectives 1 Summer

More information

Confidence Intervals (Review)

Confidence Intervals (Review) Intro to Hypothesis Tests Solutions STAT-UB.0103 Statistics for Business Control and Regression Models Confidence Intervals (Review) 1. Each year, construction contractors and equipment distributors from

More information

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing

Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing Business Statistics, 9e (Groebner/Shannon/Fry) Chapter 9 Introduction to Hypothesis Testing 1) Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures

More information

Interpreting Data in Normal Distributions

Interpreting Data in Normal Distributions Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,

More information

Binomial Distribution Problems. Binomial Distribution SOLUTIONS. Poisson Distribution Problems

Binomial Distribution Problems. Binomial Distribution SOLUTIONS. Poisson Distribution Problems 1 Binomial Distribution Problems (1) A company owns 400 laptops. Each laptop has an 8% probability of not working. You randomly select 20 laptops for your salespeople. (a) What is the likelihood that 5

More information

LAB 4: APPROXIMATING REAL ZEROS OF POLYNOMIAL FUNCTIONS

LAB 4: APPROXIMATING REAL ZEROS OF POLYNOMIAL FUNCTIONS LAB 4: APPROXIMATING REAL ZEROS OF POLYNOMIAL FUNCTIONS Objectives: 1. Find real zeros of polynomial functions. 2. Solve nonlinear inequalities by graphing. 3. Find the maximum value of a function by graphing.

More information

ALGEBRA 2/ TRIGONOMETRY

ALGEBRA 2/ TRIGONOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA 2/ TRIGONOMETRY Wednesday, June 18, 2014 1:15 4:15 p.m. SAMPLE RESPONSE SET Table of Contents Question 28...................

More information

Using Your TI-NSpire Calculator: Normal Distributions Dr. Laura Schultz Statistics I

Using Your TI-NSpire Calculator: Normal Distributions Dr. Laura Schultz Statistics I Using Your TI-NSpire Calculator: Normal Distributions Dr. Laura Schultz Statistics I Always start by drawing a sketch of the normal distribution that you are working with. Shade in the relevant area (probability),

More information

Hypothesis Testing. Bluman Chapter 8

Hypothesis Testing. Bluman Chapter 8 CHAPTER 8 Learning Objectives C H A P T E R E I G H T Hypothesis Testing 1 Outline 8-1 Steps in Traditional Method 8-2 z Test for a Mean 8-3 t Test for a Mean 8-4 z Test for a Proportion 8-5 2 Test for

More information

Session 7 Bivariate Data and Analysis

Session 7 Bivariate Data and Analysis Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares

More information

Density Determinations and Various Methods to Measure

Density Determinations and Various Methods to Measure Density Determinations and Various Methods to Measure Volume GOAL AND OVERVIEW This lab provides an introduction to the concept and applications of density measurements. The densities of brass and aluminum

More information

The Density of Liquids and Solids

The Density of Liquids and Solids The Density of Liquids and Solids Objectives The objectives of this laboratory are: a) To determine the density of pure water; b) To determine the density of aluminum (applying the technique of water displacement)

More information

AP Statistics 2009 Scoring Guidelines Form B

AP Statistics 2009 Scoring Guidelines Form B AP Statistics 2009 Scoring Guidelines Form B The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded

More information

Solutions to Worksheet on Hypothesis Tests

Solutions to Worksheet on Hypothesis Tests s to Worksheet on Hypothesis Tests. A production line produces rulers that are supposed to be inches long. A sample of 49 of the rulers had a mean of. and a standard deviation of.5 inches. The quality

More information

Chapter 3: Data Description Numerical Methods

Chapter 3: Data Description Numerical Methods Chapter 3: Data Description Numerical Methods Learning Objectives Upon successful completion of Chapter 3, you will be able to: Summarize data using measures of central tendency, such as the mean, median,

More information

PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY

PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY The Student Handout is page 11. Give this page to students as a separate sheet. Area of Circles and Squares Circumference and Perimeters Volume of Cylinders

More information

32 Measures of Central Tendency and Dispersion

32 Measures of Central Tendency and Dispersion 32 Measures of Central Tendency and Dispersion In this section we discuss two important aspects of data which are its center and its spread. The mean, median, and the mode are measures of central tendency

More information