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ELEMENTARY STATISTICS 3E
William Navidi and Barry Monk
©McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.
Applications of the Normal
Distribution
Section 7.2
©McGraw-Hill Education.
Objectives
1. Convert values from a normal distribution to 𝑧-scores
2. Find areas under a normal curve
3. Find the value from a normal distribution corresponding to a
given proportion
©McGraw-Hill Education.
Objective 1
Convert values from a normal distribution to
𝑧-scores
©McGraw-Hill Education.
Standardization
Recall that the 𝑧-score of a data value
represents the number of standard
deviations that data value is above or
below the mean.
If 𝑥 is a value from a normal distribution
with mean 𝜇 and standard deviation 𝜎,
we can convert 𝑥 to a 𝑧-score by using a
method known as standardization. The
𝑥−𝜇
𝑧-score of 𝑥 is 𝑧 =
.
𝜎
For example, consider a woman whose
height is 𝑥 = 67 inches from a normal
population with mean 𝜇 = 64 inches and
𝜎 = 3 inches. The 𝑧-score is:
𝑥 − 𝜇 67 − 64
𝑧=
=
=1
𝜎
3
©McGraw-Hill Education.
Objective 2
Find areas under a normal curve
*(TI-84 PLUS)
©McGraw-Hill Education.
Ex 1: Area Under a Normal Curve (TI-84)
A study reported that the length of pregnancy from conception to birth
is approximately normally distributed with mean 𝜇 = 272 days and
standard deviation 𝜎 = 9 days. What proportion of pregnancies last
longer than 280 days?
Solution:
We use the normalcdf command with 280
as the lower endpoint, 1E99 as the upper
endpoint, 272 as the mean, and 9 as the
standard deviation. We conclude that the
proportion of pregnancies that last longer
than 280 days is 0.1870.
©McGraw-Hill Education.
Ex 2: Area Under a Normal Curve (TI-84)
The length of a pregnancy from conception to birth is approximately
normally distributed with mean 𝜇 = 272 days and standard deviation
𝜎 = 9 days. A pregnancy is considered full-term if it lasts between 252
days and 298 days. What proportion of pregnancies are full-term?
Solution:
We use the normalcdf command with 252
as the lower endpoint, 298 as the upper
endpoint, 272 as the mean, and 9 as the
standard deviation. The proportion of
pregnancies that are full-term, between
252 days and 298 days, is 0.9849.
©McGraw-Hill Education.
Objective 3*
Find the value from a normal distribution
corresponding to a given proportion
*(TI-84 PLUS)
©McGraw-Hill Education.
Example: Finding Normal Values (TI-84)
Mensa is an organization whose membership is limited to people whose IQ
is in the top 2% of the population. Assume that scores on an IQ test are
normally distributed with mean 𝜇 = 100 and standard deviation 𝜎 = 15.
What is the minimum score needed to qualify for membership in Mensa?
Solution:
The figure shows the value 𝑥 separating the upper
2% from the lower 98%. The area 0.02 is on the
right, so we subtract from 1 and work with the
area 0.98 on the left.
Using the invNorm command with 0.98 as the area
on the left, 100 as the mean, and 15 as the
standard deviation, we find the minimum score to
be 130.81. Since IQ scores are generally whole
numbers, we round this to 𝑥 = 131.
©McGraw-Hill Education.
You Should Know . . .
• How to convert values from a normal distribution to 𝑧scores
• How to find areas under a normal curve (Calculator)
• How to find the value from a normal population
corresponding to a given proportion (Calculator)
©McGraw-Hill Education.
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MATH 117 Arizona State University Algebraic Functions & Graphs Exam Practice
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What are the frequency and percentage of the COPD patients in the severe airfl ow limitation group who are employed in the Eckblad et al 2014 study
1. What are the frequency and percentage of the COPD patients in the severe airfl ow limitation group who are employed in ...
What are the frequency and percentage of the COPD patients in the severe airfl ow limitation group who are employed in the Eckblad et al 2014 study
1. What are the frequency and percentage of the COPD patients in the severe airfl ow limitation group who are employed in the Eckerblad et al. (2014) study? 2. What percentage of the total sample is retired? What percentage of the total sample is on sick leave? 3. What is the total sample size of this study? What frequency and percentage of the total sample were still employed? Show your calculations and round your answer to the nearest whole percent.4. What is the total percentage of the sample with a smoking history—either still smoking or former smokers? Is the smoking history for study participants clinically important? Provide a rationale for your answer.5. What are pack years of smoking? Is there a signifi cant difference between the moderate and severe airfl ow limitation groups regarding pack years of smoking? Provide a rationale for your answer. 6. What were the four most common psychological symptoms reported by this sample of patients with COPD? What percentage of these subjects experienced these symptoms? Was there a sig-nifi cant difference between the moderate and severe airfl ow limitation groups for psychological symptoms? 7. What frequency and percentage of the total sample used short-acting β 2 -agonists? Show your calculations and round to the nearest whole percent.8. Is there a signifi cant difference between the moderate and severe airfl ow limitation groups regarding the use of short-acting β 2 -agonists? Provide a rationale for your answer. 9. Was the percentage of COPD patients with moderate and severe airflow limitation using short-acting β 2 -agonists what you expected? Provide a rationale with documentation for your answer. 10. Are these findings ready for use in practice? Provide a rationale for your answer.1. The number of nursing students enrolled in a particular nursing program between the years of 2010 and 2016, respectively, were 563, 593, 606, 520, 563, 610, and 577. Determine the mean ( X ), median ( MD ), and mode of the number of the nursing students enrolled in this program. Show your calculations. 2. What is the mode for the variable inpatient complications in Table 2 of the Winkler et al. (2014) study? What percentage of the study participants had this complication? 3. Does the distribution of inpatient complications have a single mode, or is this distribution bimodal or multimodal? Provide a rationale for your answer.4. As reported in Table 1 , what are the three most common cardiovascular medical history events in this study, and why is it clinically important to know the frequency of these events?5. What are the mean and median lengths of stay (LOS) for the study participants? 6. Are the mean and median for LOS similar or different? What might this indicate about the distribution of the sample? Provide a rationale for your answer. 7. Examine the study results and determine the mode for arrhythmias experienced by the particiants. What was the second most common arrhythmia in this sample? 8. Was the most common arrhythmia in Question 7 related to LOS? Was this result statistically significant? Provide a rationale for your answer.9. What study variables were independently predictive of the 50 premature ventricular contractions (PVCs) per hour in this study? 10. In Table 1 , what race is the mode for this sample? Should these study findings be generalized to American Indians with ACS? Provide a rationale for your answer.1. What were the name and type of measurement method used to measure Caring Practices in the Roch, Dubois, and Clarke (2014) study? 2. The data collected with the scale identified in Questions 1 were at what level of measurement? Provide a rationale for your answer.3. What were the subscales included in the CNPISS used to measure RNs ’ perceptions of their Caring Practices? Do these subscales seem relevant? Document your answer.4. Which subscale for Caring Practices had the lowest mean? What does this result indicate?5. What were the dispersion results for the Relational Care subscale of the Caring Practices in Table 2 ? What do these results indicate? 6. Which subscale of Caring Practices has the lowest dispersion or variation of scores? Provide a rationale for your answer. 7. Which subscale of Caring Practices had the highest mean? What do these results indicate?8. Compare the Overall rating for Organizational Climate with the Overall rating of Caring Practices. What do these results indicate? 9. The response rate for the survey in this study was 45%. Is this a study strength or limitation? Provide a rationale for your answer. 10. What conclusions did the researchers make regarding the caring practices of the nurses in this study? How might these results affect your practice?

statistics
Week 3 Project - STAT 3001 Student Name: <Type your name here> Date:<Enter the date on which you began workin ...
statistics
Week 3 Project - STAT 3001 Student Name: <Type your name here> Date:<Enter the date on which you began working on this assignment.> Instructions:To complete this project, you will need the following materials: STAT DISK User Manual (found in the classroom in Doc Sharing)Access to the Internet to download the STATDISK program. Part I.Analyze Data Instructions Answers Open the file Car Measurements using menu option Datasets and then Elementary Stats, 13th Edition.This file contains information on a number of measurements related to cars. How many observations are there in this file? 2-5 Analyze the data in this file and complete the following table, indicating for each variable what type of data it represents. Variable Qualitative/ Quantitative Discrete/ Continuous/ Neither Level of Measurement Size Braking (distance) City (MPG) Car 6. Would you consider this data to represent a sample or a population? Why? Part II. ScatterPlots 7. Create a scatterplot for the data in the Length (inches) and Braking distance (feet) columns.Paste it here.You may need to resize the plot once it is in this file. 8. Explain the visual relationship between Length and Braking distance. 9. Create a scatterplot for the data in Displacement (liters) and Highway (MPG) columns. Paste it here. You may need to resize the plot once it is in this file. 10. Explain the visual relationship between Displacement and Highway MPG. Part III.Correlation 11.Using Stat Disk, calculate the linear correlation between the data in the Length and Braking distance columns. List the steps used for the calculation and give the resulting correlation coefficient. 12.Explain the mathematical relationship between Length and Braking distance based on the linear correlation coefficient.Be certain to include comments about the magnitude and the direction of the correlation. 13.List the sample size and the degrees of freedom for this computation. 14.Using Stat Disk, calculate the linear correlation coefficient between the data in the Displacement and Highway MPG columns. 15.Compare and contrast these two relationships: Length and Braking distance Displacement and Highway MPG How are they similar? How are they different? [Hint: Read Page 290 “Types of Correlation”] Part IV.Simple Regression Let’s say that we wanted to be able to predict the city MPG of a car based on its Weight in pounds. Using this sample data, perform a simple-linear regression to determine the line-of-best fit. Use the Weight as your x (independent) variable and City MPG as your y (response) variable. Use 3 places after the decimal in your answer. Refer to page 13 in the Stat Disk User’s Manual. 16. Paste your results here: Answer the following questions related to this simple regression 17. What is the equation of the line-of-best fit?Insert the values for bo and b1 from above into y = bo + b1x. 18. What is the slope of the line?What does it tell you about the relationship between the Weight and City MPG data? Be sure to specify the proper units. 19.What is the y-intercept of the line?What does it tell you about the relationship between Weight and City MPG? 20. Using the regression equation, what would you predict for the City MPG of a car weighing 2250 pounds? Show your calculation and round to the nearest tenth. 21. Using the regression equation, let’s say you have a car with a City MPG of 29, what would the car weigh? Round to the nearest whole number. 22. Find the coefficient of determination (R2 value) for this data.What does this tell you about this relationship? [Hint:see definition on Page 311.] Part V.Multiple Regression Let’s say that we wanted to be able to predict the Highway MPG of a car based on DisplacementLengthBraking Using this sample data, perform a multiple-regression using Displacement, Length, Braking distance with Highway MPG as the dependent variable. Refer to page 14 in the Stat Disk User’s Manual. 23. Paste your results here: 24. What is the equation of the line-of-best fit?The form of the equation is Y = bo + b1X1 + b2X2 + b3X3 (fill in values for b0, b1, b2, and b3). [Round coefficients to 2 decimal places.] 25. Using the multiple regression equation, what would you predict for the Highway MPG of a car whose Length in inches is 184Braking distance in feet is 139Displacement in liters is 2.2 Round to the nearest tenth. 26. What is the R2 value for this regression?What does it tell you about the regression? Submit your final draft of your Word file by going to Week 3, Project, and follow the directions under Week 3 Assignment 2.Please use the naming convention "WK3Assgn2+first initial+last name" as the Submission Title.
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Module 6 Analysis of Research
Details:Doctoral researchers must be able to analyze research studies to determine their significance and contribution to ...
Module 6 Analysis of Research
Details:Doctoral researchers must be able to analyze research studies to determine their significance and contribution to the body of knowledge. This assignment will allow you to practice your skills in analyzing research studies.General Requirements:Use the following information to ensure successful completion of the assignment:Read the following sections of "Using Teacher-Written Praise Notes to Promote a Positive Environment in a Middle School": the Abstract, Introduction, Participants and Setting, Procedure, Measures (paragraph 1 only), Data Analysis (paragraph 1 only), Results (paragraph 1 only), and Discussion (paragraphs 1 and 2 only).This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.Doctoral learners are required to use APA style for their writing assignments. The APA Style Guide is located in the Student Success Center.This assignment requires that at least two additional scholarly research sources related to this topic, and at least one in-text citation from each source be included.Directions:In an essay (250-500 words), use the scenario presented above to answer the following questions:What statistical test was used in "Using Teacher-Written Praise Notes to Promote a Positive Environment in a Middle School?"Did the authors use the correct statistical test? In other words, what was their rationale for using this test (i.e., were the variables discrete or continuous and was the test appropriate for this type of data?)What was the research question? How did the statistical test address and answer the research question?How did the authors interpret the results of this studyPlease respond to the above question using the requirements as referenced above. Please also cite the reference in APA 6th edition format.

MATH 117 Arizona State University Algebraic Functions & Graphs Exam Practice
i will send pictures of the questions on my math test and i just need help with some of the answers
MATH 117 Arizona State University Algebraic Functions & Graphs Exam Practice
i will send pictures of the questions on my math test and i just need help with some of the answers

What are the frequency and percentage of the COPD patients in the severe airfl ow limitation group who are employed in the Eckblad et al 2014 study
1. What are the frequency and percentage of the COPD patients in the severe airfl ow limitation group who are employed in ...
What are the frequency and percentage of the COPD patients in the severe airfl ow limitation group who are employed in the Eckblad et al 2014 study
1. What are the frequency and percentage of the COPD patients in the severe airfl ow limitation group who are employed in the Eckerblad et al. (2014) study? 2. What percentage of the total sample is retired? What percentage of the total sample is on sick leave? 3. What is the total sample size of this study? What frequency and percentage of the total sample were still employed? Show your calculations and round your answer to the nearest whole percent.4. What is the total percentage of the sample with a smoking history—either still smoking or former smokers? Is the smoking history for study participants clinically important? Provide a rationale for your answer.5. What are pack years of smoking? Is there a signifi cant difference between the moderate and severe airfl ow limitation groups regarding pack years of smoking? Provide a rationale for your answer. 6. What were the four most common psychological symptoms reported by this sample of patients with COPD? What percentage of these subjects experienced these symptoms? Was there a sig-nifi cant difference between the moderate and severe airfl ow limitation groups for psychological symptoms? 7. What frequency and percentage of the total sample used short-acting β 2 -agonists? Show your calculations and round to the nearest whole percent.8. Is there a signifi cant difference between the moderate and severe airfl ow limitation groups regarding the use of short-acting β 2 -agonists? Provide a rationale for your answer. 9. Was the percentage of COPD patients with moderate and severe airflow limitation using short-acting β 2 -agonists what you expected? Provide a rationale with documentation for your answer. 10. Are these findings ready for use in practice? Provide a rationale for your answer.1. The number of nursing students enrolled in a particular nursing program between the years of 2010 and 2016, respectively, were 563, 593, 606, 520, 563, 610, and 577. Determine the mean ( X ), median ( MD ), and mode of the number of the nursing students enrolled in this program. Show your calculations. 2. What is the mode for the variable inpatient complications in Table 2 of the Winkler et al. (2014) study? What percentage of the study participants had this complication? 3. Does the distribution of inpatient complications have a single mode, or is this distribution bimodal or multimodal? Provide a rationale for your answer.4. As reported in Table 1 , what are the three most common cardiovascular medical history events in this study, and why is it clinically important to know the frequency of these events?5. What are the mean and median lengths of stay (LOS) for the study participants? 6. Are the mean and median for LOS similar or different? What might this indicate about the distribution of the sample? Provide a rationale for your answer. 7. Examine the study results and determine the mode for arrhythmias experienced by the particiants. What was the second most common arrhythmia in this sample? 8. Was the most common arrhythmia in Question 7 related to LOS? Was this result statistically significant? Provide a rationale for your answer.9. What study variables were independently predictive of the 50 premature ventricular contractions (PVCs) per hour in this study? 10. In Table 1 , what race is the mode for this sample? Should these study findings be generalized to American Indians with ACS? Provide a rationale for your answer.1. What were the name and type of measurement method used to measure Caring Practices in the Roch, Dubois, and Clarke (2014) study? 2. The data collected with the scale identified in Questions 1 were at what level of measurement? Provide a rationale for your answer.3. What were the subscales included in the CNPISS used to measure RNs ’ perceptions of their Caring Practices? Do these subscales seem relevant? Document your answer.4. Which subscale for Caring Practices had the lowest mean? What does this result indicate?5. What were the dispersion results for the Relational Care subscale of the Caring Practices in Table 2 ? What do these results indicate? 6. Which subscale of Caring Practices has the lowest dispersion or variation of scores? Provide a rationale for your answer. 7. Which subscale of Caring Practices had the highest mean? What do these results indicate?8. Compare the Overall rating for Organizational Climate with the Overall rating of Caring Practices. What do these results indicate? 9. The response rate for the survey in this study was 45%. Is this a study strength or limitation? Provide a rationale for your answer. 10. What conclusions did the researchers make regarding the caring practices of the nurses in this study? How might these results affect your practice?

statistics
Week 3 Project - STAT 3001 Student Name: <Type your name here> Date:<Enter the date on which you began workin ...
statistics
Week 3 Project - STAT 3001 Student Name: <Type your name here> Date:<Enter the date on which you began working on this assignment.> Instructions:To complete this project, you will need the following materials: STAT DISK User Manual (found in the classroom in Doc Sharing)Access to the Internet to download the STATDISK program. Part I.Analyze Data Instructions Answers Open the file Car Measurements using menu option Datasets and then Elementary Stats, 13th Edition.This file contains information on a number of measurements related to cars. How many observations are there in this file? 2-5 Analyze the data in this file and complete the following table, indicating for each variable what type of data it represents. Variable Qualitative/ Quantitative Discrete/ Continuous/ Neither Level of Measurement Size Braking (distance) City (MPG) Car 6. Would you consider this data to represent a sample or a population? Why? Part II. ScatterPlots 7. Create a scatterplot for the data in the Length (inches) and Braking distance (feet) columns.Paste it here.You may need to resize the plot once it is in this file. 8. Explain the visual relationship between Length and Braking distance. 9. Create a scatterplot for the data in Displacement (liters) and Highway (MPG) columns. Paste it here. You may need to resize the plot once it is in this file. 10. Explain the visual relationship between Displacement and Highway MPG. Part III.Correlation 11.Using Stat Disk, calculate the linear correlation between the data in the Length and Braking distance columns. List the steps used for the calculation and give the resulting correlation coefficient. 12.Explain the mathematical relationship between Length and Braking distance based on the linear correlation coefficient.Be certain to include comments about the magnitude and the direction of the correlation. 13.List the sample size and the degrees of freedom for this computation. 14.Using Stat Disk, calculate the linear correlation coefficient between the data in the Displacement and Highway MPG columns. 15.Compare and contrast these two relationships: Length and Braking distance Displacement and Highway MPG How are they similar? How are they different? [Hint: Read Page 290 “Types of Correlation”] Part IV.Simple Regression Let’s say that we wanted to be able to predict the city MPG of a car based on its Weight in pounds. Using this sample data, perform a simple-linear regression to determine the line-of-best fit. Use the Weight as your x (independent) variable and City MPG as your y (response) variable. Use 3 places after the decimal in your answer. Refer to page 13 in the Stat Disk User’s Manual. 16. Paste your results here: Answer the following questions related to this simple regression 17. What is the equation of the line-of-best fit?Insert the values for bo and b1 from above into y = bo + b1x. 18. What is the slope of the line?What does it tell you about the relationship between the Weight and City MPG data? Be sure to specify the proper units. 19.What is the y-intercept of the line?What does it tell you about the relationship between Weight and City MPG? 20. Using the regression equation, what would you predict for the City MPG of a car weighing 2250 pounds? Show your calculation and round to the nearest tenth. 21. Using the regression equation, let’s say you have a car with a City MPG of 29, what would the car weigh? Round to the nearest whole number. 22. Find the coefficient of determination (R2 value) for this data.What does this tell you about this relationship? [Hint:see definition on Page 311.] Part V.Multiple Regression Let’s say that we wanted to be able to predict the Highway MPG of a car based on DisplacementLengthBraking Using this sample data, perform a multiple-regression using Displacement, Length, Braking distance with Highway MPG as the dependent variable. Refer to page 14 in the Stat Disk User’s Manual. 23. Paste your results here: 24. What is the equation of the line-of-best fit?The form of the equation is Y = bo + b1X1 + b2X2 + b3X3 (fill in values for b0, b1, b2, and b3). [Round coefficients to 2 decimal places.] 25. Using the multiple regression equation, what would you predict for the Highway MPG of a car whose Length in inches is 184Braking distance in feet is 139Displacement in liters is 2.2 Round to the nearest tenth. 26. What is the R2 value for this regression?What does it tell you about the regression? Submit your final draft of your Word file by going to Week 3, Project, and follow the directions under Week 3 Assignment 2.Please use the naming convention "WK3Assgn2+first initial+last name" as the Submission Title.
9 pages

General Social Survey
The General Social Survey is a survey of the people of America of what they think about the national issue such as nationa ...
General Social Survey
The General Social Survey is a survey of the people of America of what they think about the national issue such as national spending priorities, ...
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