Elementary Statistics: A Step By Step Approach
Elementary Statistics: A Step By Step Approach
9th Edition
ISBN: 9780073534985
Author: Allan Bluman
Publisher: McGraw-Hill Science/Engineering/Math
Question
Chapter 6, Problem 6.1.1RE

a.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 1.95. That is, P(0z1.95) .

a.

Expert Solution
Check Mark

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

Explanation of Solution

Given info:

The z values are 0 and 1.95.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 2.06with the help of following instructions:

  • Select Graph > Probability Distribution Plot > View Probability >OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Enter the Mean as 0.0 and Standard deviation as 1.0.
  • Choose the tab for Shaded Area, then X Value.
  • Click the picture for Middle.
  • Type in the smaller value 0 for X value1 and then the larger value 1.95 for the X value2.
  • Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 6.1.1RE , additional homework tip  1

Therefore, P(0z1.95)=0.4744.

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 1.95 is 0.4744.

b.

To determine

To find: The area under the standard normal distribution curve for z lying between 0 and 0.37. That is, P(0z0.37) .

b.

Expert Solution
Check Mark

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

Explanation of Solution

Given info:

The z values are 0 and 0.37.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 0 and 0.37 with the help of following instructions:

  • Select Graph > Probability Distribution Plot > View Probability >OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Enter the Mean as 0.0 and Standard deviation as 1.0.
  • Choose the tab for Shaded Area, then X Value.
  • Click the picture for Middle.
  • Type in the smaller value 0 for X value1 and then the larger value 0.37 for the X value2.
  • Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 6.1.1RE , additional homework tip  2

Therefore, P(0z0.37)=0.1443 .

Conclusion:

The area under the standard normal distribution curve for z lying between 0 and 0.37 is 0.1443.

c.

To determine

To find: The area under the standard normal distribution curve for z lying between 1.32 and 1.82. That is, P(1.32z1.82) .

c.

Expert Solution
Check Mark

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

Explanation of Solution

Given info:

The z values are 1.32 and 1.82.

Calculation:

Software procedure:

Step by step procedure to find the area under the normal curve between 1.32 and 1.82 with the help of following instructions:

  • Select Graph > Probability Distribution Plot > View Probability >OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Enter the Mean as 0.0 and Standard deviation as 1.0.
  • Choose the tab for Shaded Area, then X Value.
  • Click the picture for Middle.
  • Type in the smaller value 1.32 for X value1 and then the larger value 1.82 for the X value2.
  • Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 6.1.1RE , additional homework tip  3

Therefore, P(1.32z1.82)=0.05904 .

Conclusion:

The area under the standard normal distribution curve for z lying between 1.32 and 1.82 is 0.05904.

d.

To determine

To find: The area under the standard normal distribution curve for z lying between –1.05 and 2.05. That is, P(1.05z2.05) .

d.

Expert Solution
Check Mark

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

Explanation of Solution

Given info:

The z values are –1.05 and 2.05.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -1.05 and 2.05 with the help of following instructions:

  • Select Graph > Probability Distribution Plot > View Probability >OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Enter the Mean as 0.0 and Standard deviation as 1.0.
  • Choose the tab for Shaded Area, then X Value.
  • Click the picture for Middle.
  • Type in the smaller value −1.05 for X value1 and then the larger value 2.05 for the X value2.
  • Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 6.1.1RE , additional homework tip  4

Therefore, P(1.05z2.05)=0.8330 .

Conclusion:

The area under the standard normal distribution curve for z lying between –1.05 and 2.05 is 0.8330.

e.

To determine

To find: The area under the standard normal distribution curve for z lying between -0.03 and 0.53. That is, P(0.03z0.53)

e.

Expert Solution
Check Mark

Answer to Problem 6.1.1RE

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Explanation of Solution

Given info:

The z values are -0.03 and 0.53.

Calculation:

Software procedure:

Step by step procedure to; find the area under the normal curve between -0.07 and 0.49 with the help of following instructions:

  • Select Graph > Probability Distribution Plot > View Probability >OK.
  • From Distribution, choose ‘Normal’ distribution.
  • Enter the Mean as 0.0 and Standard deviation as 1.0.
  • Choose the tab for Shaded Area, then X Value.
  • Click the picture for Middle.
  • Type in the smaller value −0.03 for X value1 and then the larger value 0.53 for the X value2.
  • Click OK.

Output using the MINITAB software is given below:

Elementary Statistics: A Step By Step Approach, Chapter 6, Problem 6.1.1RE , additional homework tip  5

Therefore, P(0.03z0.53)=0.2139 .

Conclusion:

The area under the standard normal distribution curve for z lying between −0.03 and 0.53 is 0.2139.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 6 Solutions

Elementary Statistics: A Step By Step Approach

Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 11ECh. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 13ECh. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 17ECh. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 21ECh. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 23ECh. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - For Exercises 7 through 26, find the area under...Ch. 6.1 - Prob. 27ECh. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - Prob. 29ECh. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - Prob. 31ECh. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - Prob. 33ECh. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - Prob. 37ECh. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - In Exercises 27 through 40, find the probabilities...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - For Exercises 41 through 46, find the z value that...Ch. 6.1 - Find the z value to the left of the mean so that...Ch. 6.1 - Find the z value to the right of the mean so that...Ch. 6.1 - Find two z values, one positive and one negative,...Ch. 6.1 - Find two z values so that 48% of the middle area...Ch. 6.1 - Prob. 51ECCh. 6.1 - Prob. 52ECCh. 6.1 - Prob. 53ECCh. 6.1 - For Exercises 5356, z0 is the statistical notation...Ch. 6.1 - Prob. 55ECCh. 6.1 - Prob. 56ECCh. 6.1 - Prob. 57ECCh. 6.1 - Prob. 58ECCh. 6.1 - Prob. 59ECCh. 6.1 - Find P(z 2.3 and z 1.2).Ch. 6.2 - Applying the Concepts 62 Smart People Assume you...Ch. 6.2 - Prob. 1ECh. 6.2 - Teachers Salaries The average annual salary for...Ch. 6.2 - Population in U.S. Jails The average daily jail...Ch. 6.2 - SAT Scores The national average SAT score (for...Ch. 6.2 - Chocolate Bar Calories The average number of...Ch. 6.2 - Monthly Mortgage Payments The average monthly...Ch. 6.2 - Prob. 7ECh. 6.2 - Doctoral Student Salaries Full-time Ph.D. students...Ch. 6.2 - Miles Driven Annually The mean number of miles...Ch. 6.2 - Commute Time to Work The average commute to work...Ch. 6.2 - Credit Card Debt The average credit card debt for...Ch. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Newborn Elephant Weights Newborn elephant calves...Ch. 6.2 - Prob. 15ECh. 6.2 - Salary of Full Professors The average salary of a...Ch. 6.2 - Prob. 17ECh. 6.2 - Itemized Charitable Contributions The average...Ch. 6.2 - New Home Sizes A contractor decided to build homes...Ch. 6.2 - New-Home Prices If the average price of a new...Ch. 6.2 - Cost of Personal Computers The average price of a...Ch. 6.2 - Reading Improvement Program To help students...Ch. 6.2 - Prob. 23ECh. 6.2 - Ages of Amtrak Passenger Cars The average age of...Ch. 6.2 - Lengths of Hospital Stays The average length of a...Ch. 6.2 - High School Competency Test A mandatory competency...Ch. 6.2 - Product Marketing An advertising company plans to...Ch. 6.2 - Prob. 28ECh. 6.2 - Wristwatch Lifetimes The mean lifetime of a...Ch. 6.2 - Police Academy Acceptance Exams To qualify for a...Ch. 6.2 - In the distributions shown, state the mean and...Ch. 6.2 - SAT Scores Suppose that the mathematics SAT scores...Ch. 6.2 - Prob. 33ECh. 6.2 - Standardizing If a distribution of raw scores were...Ch. 6.2 - Social Security Payments Consider the distribution...Ch. 6.2 - Find the Mean In a normal distribution, find when...Ch. 6.2 - Internet Users U.S. internet users spend an...Ch. 6.2 - Exam Scores An instructor gives a 100-point...Ch. 6.2 - Drive-in Movies The data shown represent the...Ch. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Prob. 43ECh. 6.3 - Applying the Concepts 63 Times To Travel to School...Ch. 6.3 - Prob. 1ECh. 6.3 - Why do most of the sample means differ somewhat...Ch. 6.3 - What is the mean of the sample means?Ch. 6.3 - What is the standard deviation of the sample means...Ch. 6.3 - What does the central limit theorem say about the...Ch. 6.3 - What formula is used to gain information about an...Ch. 6.3 - Prob. 7ECh. 6.3 - Glass Garbage Generation A survey found that the...Ch. 6.3 - Prob. 9ECh. 6.3 - Teachers Salaries in Connecticut The average...Ch. 6.3 - Prob. 11ECh. 6.3 - Teachers Salaries in North Dakota The average...Ch. 6.3 - Prob. 13ECh. 6.3 - SAT Scores The national average SAT score (for...Ch. 6.3 - Cost of Overseas Trip The average overseas trip...Ch. 6.3 - Cell Phone Lifetimes A recent study of the...Ch. 6.3 - Water Use The Old Farmers Almanac reports that the...Ch. 6.3 - Medicare Hospital Insurance The average yearly...Ch. 6.3 - Amount of Laundry Washed Each Year Procter Gamble...Ch. 6.3 - Per Capita Income of Delaware Residents In a...Ch. 6.3 - Prob. 21ECh. 6.3 - Systolic Blood Pressure Assume that the mean...Ch. 6.3 - Cholesterol Content The average cholesterol...Ch. 6.3 - Ages of Proofreaders At a large publishing...Ch. 6.3 - TIMSS Test On the Trends in International...Ch. 6.3 - Life Expectancies In a study of the life...Ch. 6.3 - Home Values A study of 800 homeowners in a certain...Ch. 6.3 - Breaking Strength of Steel Cable The average...Ch. 6.3 - Prob. 29ECCh. 6.3 - Prob. 30ECCh. 6.4 - Applying the Concepts 64 Mountain Climbing Safety...Ch. 6.4 - Explain why a normal distribution can be used as...Ch. 6.4 - What conditions must be met to use the normal...Ch. 6.4 - Why is a correction for continuity necessary?Ch. 6.4 - When is the normal distribution not a good...Ch. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Check each binomial distribution to see whether it...Ch. 6.4 - Check each binomial distribution to see whether it...Ch. 6.4 - Prob. 9ECh. 6.4 - School Enrollment Of all 3- to 5-year-old...Ch. 6.4 - Home Ownership In a recent year, the rate of U.S....Ch. 6.4 - Mail Order A mail order company has an 8% success...Ch. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 15ECh. 6.4 - Population of College Cities College students...Ch. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Female Americans Who Have Completed 4 Years of...Ch. 6.4 - Prob. 20ECh. 6.4 - Elementary School Teachers Women comprise 80.3% of...Ch. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECCh. 6 - Prob. 6.1.1RECh. 6 - Find the area under the standard normal...Ch. 6 - Prob. 6.1.3RECh. 6 - Using the standard normal distribution, find each...Ch. 6 - Per Capita Spending on Health Care The average per...Ch. 6 - Prob. 6.2.6RECh. 6 - Commuter Train Passengers On a certain run of a...Ch. 6 - Monthly Spending for Paging and Messaging Services...Ch. 6 - Cost of Smartphone Repair The average cost of...Ch. 6 - Prob. 6.2.10RECh. 6 - Private Four-Year College Enrollment A random...Ch. 6 - Heights of Active Volcanoes The heights (in feet...Ch. 6 - Confectionary Products Americans ate an average of...Ch. 6 - Average Precipitation For the first 7 months of...Ch. 6 - Sodium in Frozen Food The average number of...Ch. 6 - Prob. 6.3.16RECh. 6 - Retirement Income Of the total population of...Ch. 6 - Slot Machines The probability of winning on a slot...Ch. 6 - Multiple-Job Holders According to the government,...Ch. 6 - Enrollment in Personal Finance Course In a large...Ch. 6 - Prob. 6.4.21RECh. 6 - Larceny-Thefts Excluding motor vehicle thefts, 26%...Ch. 6 - Determine whether each statement is true or false....Ch. 6 - Prob. 2CQCh. 6 - Determine whether each statement is true or false....Ch. 6 - The z value corresponding to a number below the...Ch. 6 - Determine whether each statement is true or false....Ch. 6 - Prob. 6CQCh. 6 - Select the best answer. 7. The mean of the...Ch. 6 - Approximately what percentage of normally...Ch. 6 - Which is not a property of the standard normal...Ch. 6 - When a distribution is positively skewed, the...Ch. 6 - Prob. 11CQCh. 6 - Complete the following statements with the best...Ch. 6 - The difference between a sample mean and a...Ch. 6 - The mean of the sample means equals ________.Ch. 6 - The standard deviation of all possible sample...Ch. 6 - The normal distribution can be used to approximate...Ch. 6 - Prob. 17CQCh. 6 - Find the area under the standard normal...Ch. 6 - Using the standard normal distribution, find each...Ch. 6 - Amount of Rain in a City The average amount of...Ch. 6 - Heights of People The average height of a certain...Ch. 6 - Sports Drink Consumption The average number of...Ch. 6 - Years to Complete a Graduate Program The average...Ch. 6 - Passengers on a Bus On the daily run of an express...Ch. 6 - Thickness of Library Books The average thickness...Ch. 6 - Prob. 26CQCh. 6 - Prob. 27CQCh. 6 - Electric Bills The average electric bill in a...Ch. 6 - Sleep Survey According to a recent survey, 38% of...Ch. 6 - Prob. 30CQCh. 6 - Household Online Connection The percentage of U.S....Ch. 6 - Prob. 32CQCh. 6 - Prob. 33CQCh. 6 - GMAT Scores The average GMAT scores for the top-30...Ch. 6 - Prob. 1CTCCh. 6 - Sometimes a researcher must decide whether a...Ch. 6 - Prob. 3CTCCh. 6 - Prob. 4CTCCh. 6 - Sometimes a researcher must decide whether a...Ch. 6 - Prob. 6CTCCh. 6 - Prob. 7CTCCh. 6 - Prob. 8CTCCh. 6 - Formulas Confirm the two formulas hold true for...
Knowledge Booster
Recommended textbooks for you
  • MATLAB: An Introduction with Applications
    Statistics
    ISBN:9781119256830
    Author:Amos Gilat
    Publisher:John Wiley & Sons Inc
    Probability and Statistics for Engineering and th...
    Statistics
    ISBN:9781305251809
    Author:Jay L. Devore
    Publisher:Cengage Learning
    Statistics for The Behavioral Sciences (MindTap C...
    Statistics
    ISBN:9781305504912
    Author:Frederick J Gravetter, Larry B. Wallnau
    Publisher:Cengage Learning
  • Elementary Statistics: Picturing the World (7th E...
    Statistics
    ISBN:9780134683416
    Author:Ron Larson, Betsy Farber
    Publisher:PEARSON
    The Basic Practice of Statistics
    Statistics
    ISBN:9781319042578
    Author:David S. Moore, William I. Notz, Michael A. Fligner
    Publisher:W. H. Freeman
    Introduction to the Practice of Statistics
    Statistics
    ISBN:9781319013387
    Author:David S. Moore, George P. McCabe, Bruce A. Craig
    Publisher:W. H. Freeman
  • MATLAB: An Introduction with Applications
    Statistics
    ISBN:9781119256830
    Author:Amos Gilat
    Publisher:John Wiley & Sons Inc
    Probability and Statistics for Engineering and th...
    Statistics
    ISBN:9781305251809
    Author:Jay L. Devore
    Publisher:Cengage Learning
    Statistics for The Behavioral Sciences (MindTap C...
    Statistics
    ISBN:9781305504912
    Author:Frederick J Gravetter, Larry B. Wallnau
    Publisher:Cengage Learning
    Elementary Statistics: Picturing the World (7th E...
    Statistics
    ISBN:9780134683416
    Author:Ron Larson, Betsy Farber
    Publisher:PEARSON
    The Basic Practice of Statistics
    Statistics
    ISBN:9781319042578
    Author:David S. Moore, William I. Notz, Michael A. Fligner
    Publisher:W. H. Freeman
    Introduction to the Practice of Statistics
    Statistics
    ISBN:9781319013387
    Author:David S. Moore, George P. McCabe, Bruce A. Craig
    Publisher:W. H. Freeman