Description
Mary Sue is training for a 5k run. She ran for 24 minutes a shown on the graph below.
During which range did Mary Sue run the fastest?
A. between 0-4 minutes
B. between 8-14 minutes
C. between 14-16 minutes
D. between 16 and 24 minutes
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Florida National University Statistics in Health Care Paper
Students will critically analyze the readings from Chapter 3 and 4 in your textbook. This assignment is designed to help y ...
Florida National University Statistics in Health Care Paper
Students will critically analyze the readings from Chapter 3 and 4 in your textbook. This assignment is designed to help you review, critique, and apply the readings to your Health Care setting as well as become the foundation for all of your remaining assignments. You need to read the article (in the additional weekly reading resources localize in the Syllabus and also in the Lectures link) assigned for week 2 and develop a 2-3-page paper reflecting your understanding and ability to apply the readings to your Health Care Setting. Each paper must be typewritten with 12-point font and double-spaced with standard margins. Follow APA style 7th edition format when referring to the selected articles and include a reference page. EACH PAPER SHOULD INCLUDE THE FOLLOWING: 1. Introduction (25%) Provide a brief synopsis of the meaning (not a description) of each Chapter and articles you read, in your own words. 2. Your Critique (50%) What is your reaction to the content of the articles? What did you learn about Prevalence, Incidence and the relationships between them? What did you learn and how you can apply Ordinal and Categorical Variables? Did these Chapter and articles change your thoughts about comparing the extent of Disease between groups? If so, how? If not, what remained the same? 3. Conclusion (15%) Briefly summarize your thoughts & conclusion to your critique of the articles and Chapter you read.How did these articles and Chapters impact your thoughts on quantifying the extent of disease and summarizing Data Collected in the sample? Evaluation will be based on how clearly you respond to the above, in particular: a) The clarity with which you critique the articles; b) The depth, scope, and organization of your paper; and, c) Your conclusions, including a description of the impact of these articles and Chapters on any Health Care Setting.
The graph of a quadratic inequality is shown below. Use the graph to find the solutions to the inequality in terms of x.
The graph of a quadratic inequality is shown below. Use the graph to find the solutions to the inequality in terms of x.A. ...
The graph of a quadratic inequality is shown below. Use the graph to find the solutions to the inequality in terms of x.
The graph of a quadratic inequality is shown below. Use the graph to find the solutions to the inequality in terms of x.A. x ≤ -2 or x ≥ 1B. x < 2 or x > 1C. -2 ≤ x ≤ 1D. -2 < x < 1
MATH 534 KGS Wk 6 Regression & Correlation Simple Linear Regression Analysis Essay
Final Project: Regression and Correlation Analysis Use the dependent variable (labeled Y) and one of the
independ ...
MATH 534 KGS Wk 6 Regression & Correlation Simple Linear Regression Analysis Essay
Final Project: Regression and Correlation Analysis Use the dependent variable (labeled Y) and one of the
independent variables (labeled X1, X2, and X3) in the data file. Select
and use one independent variable throughout this analysis. Use Excel to
perform the regression and correlation analysis to answer the following.
The week 6 spreadsheet can be helpful in this work.Generate a scatterplot for the specified dependent variable (Y) and
the selected independent variable (X), including the graph of the "best
fit" line. Interpret.Determine the equation of the "best fit" line, which describes the
relationship between the dependent variable and the selected independent
variable.Determine the correlation coefficient. Interpret.Determine the coefficient of determination. Interpret.Test the utility of this regression model by completing a hypothesis
test of b=0 using α=0.10. Interpret results, including the p-value.Based on the findings in steps 1-5, analyze the ability of the independent variable to predict the dependent variable.Compute the confidence interval for b, using a 95% confidence level. Interpret this interval.Compute the 99% confidence interval for the dependent variable, for a
selected value of the independent variable. Each student can choose a
value to use for the independent variable (use same value in the next
step). Interpret this interval.Using the same chosen value for part (8), estimate the 99%
prediction interval for the dependent variable. Interpret this interval.What can be said about the value of the dependent variable for
values of the independent variable that are outside the range of the
sample values? Explain.Describe a business decision that could be made based on the results
of this analysis. In other words, how might the business operations
change based on these statistical results.All DeVry University policies are in effect, including the plagiarism policy.Final Project report is due by the end of Week 7.Final Project is worth 130 total points. See grading rubric below.Summarize your results from Steps 1-11 in a 3-page report.
The report should explain and interpret the results in ways that are
understandable to someone who does not know statistics.Submission: The Word document, summary report should be
submitted for questions 1-11. The Excel output can be included as an
appendix, if needed.Format for report:Summary ReportSteps 1-11 addressed with appropriate output, graphs and interpretations. Be sure to number each step 1-11.
QNT275 DeVry University Calculating Binomial Probabilities
Statistical Concepts: ProbabilityBinomial Probability Distribution Calculating Binomial Probabilities NOTE:For ...
QNT275 DeVry University Calculating Binomial Probabilities
Statistical Concepts: ProbabilityBinomial Probability Distribution Calculating Binomial Probabilities NOTE:For question 1, you will be using the same data file your instructor gave you for the Week 2 Lab. Using the data file from your instructor (same one you used for the Week 2 Lab), calculate descriptive statistics for the variable (Coin) where each of the thirty-five students in the sample flipped a coin 10 times. Round your answers to three decimal places and type the mean and the standard deviation in the grey area below.Create scatter plots for the binomial distribution when p=0.50, p=0.25, and p=0.75 (see directions above).Paste the three scatter plots in the grey area below. List the probability value for each possibility in the binomial experiment calculated at the beginning of this lab, which was calculated with the probability of a success being ½. (Complete sentences not necessary; round your answers to three decimal places.) Give the probability for the following based on the calculations in question 3 above, with the probability of a success being ½. (Complete sentences not necessary; round your answers to three decimal places.) Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ½ and n = 10. Either show your work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¼ and n = 10. Write a comparison of these statistics to those from question 5 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¾ and n = 10. Write a comparison of these statistics to those from question 6 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = Using all four of the properties of a Binomial experiment (see page 201 in the textbook) explain in a short paragraph of several complete sentences why the Coin variable from the class survey represents a binomial distribution from a binomial experiment.Compare the mean and standard deviation for the Coin variable (question 1) with those of the mean and standard deviation for the binomial distribution that was calculated by hand in question 5. Explain how they are related in a short paragraph of several complete sentences. Mean: Standard deviation: NOTE:for questions 2-7, you will NOT be using the data file your instructor gave you.Please follow the instructions given in each question. Plotting the Binomial Probabilities For the next part of the lab, open the Week 3 Excel worksheet.This will be used for the next few questions, rather than the data file used for the first question. Click on the “binomial tables” workbookType in n=10 and p=0.5; this simulates ten flips of a coin where x is counting the number of heads that occur throughout the ten flipsCreate a scatter plot, either directly in this spreadsheet (if you are comfortable with those steps), or by using the Week 1 spreadsheet and copying the data from here onto that sheet (x would be the x variable, and P(X=x) would be the y variable.Repeat steps 2 and 3 with n=10 and p=0.25Repeat steps 2 and 3 with n=10 and p=0.75In the end, you will have three scatter plots for the first question below. Calculating Descriptive Statistics Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions.Round all numeric answers to three decimal places. P(x=0) P(x=6) P(x=1) P(x=7) P(x=2) P(x=8) P(x=3) P(x=9) P(x=4) P(x=10) P(x=5) P(x≥1) P(x<0) P(x>1) P(x≤4) P(4<x ≤7) P(x<4 or x≥7) Mean = np: Standard Deviation = : Mean = np: Standard Deviation = : Comparison: Mean = np: Standard Deviation = : Comparison: NOTE:For questions 8-9, you will use the results of the previous questions. Mean from question #1: Standard deviation from question #1: Mean from question #5: Standard deviation from question #5: Comparison and explanation:
MAT 243 Correlation Coefficient Discussion
PART 1Use the link in the Jupyter Notebook activity to access your Python script. Once you have made your calculations, co ...
MAT 243 Correlation Coefficient Discussion
PART 1Use the link in the Jupyter Notebook activity to access your Python script. Once you have made your calculations, complete this discussion. The script will output answers to the questions given below. You must attach your Python script output as an HTML file and respond to the questions below.In this discussion, you will apply the statistical concepts and techniques covered in this week's reading about correlation coefficient and simple linear regression. A car rental company wants to evaluate the premise that heavier cars are less fuel efficient than lighter cars. In other words, the company expects that fuel efficiency (miles per gallon) and weight of the car (often measured in thousands of pounds) are correlated. Performing this analysis will help the company optimize its business model and charge its customers appropriately.In this discussion, you will work with a cars data set that includes two variables:Miles per gallon (coded as mpg in the data set)Weight of the car (coded as wt in the data set)The random sample will be drawn from a CSV file. This data will be unique to you, and therefore your answers will be unique as well. Run Step 1 in the Python script to generate your unique sample data.In your initial post, address the following items:You created a scatterplot of miles per gallon against weight; check to make sure it was included in your attachment. Does the graph show any trend? If yes, is the trend what you expected? Why or why not? See Step 2 in the Python script.What is the coefficient of correlation between miles per gallon and weight? What is the sign of the correlation coefficient? Does the coefficient of correlation indicate a strong correlation, weak correlation, or no correlation between the two variables? How do you know? See Step 3 in the Python script.Write the simple linear regression equation for miles per gallon as the response variable and weight as the predictor variable. How might the car rental company use this model? See Step 4 in the Python script.What is the slope coefficient? Is this coefficient significant at a 5% level of significance (alpha=0.05)? (Hint: Check the P-value, , for weight in the Python output.) See Step 4 in the Python script.In your follow-up posts to other students, review your peers' calculations and provide some analysis and interpretation:How do their plots and correlation coefficients compare with yours?Would you recommend this regression model to the car rental company? Why or why not?Remember to attach your Python output and respond to all questions in your initial and follow-up posts. Be sure to clearly communicate your ideas using appropriate terminology. Finally, be sure to review the Discussion Rubric to understand how you will be graded on this assignment.PART 2 For this project, you will submit the Python script you used to make your calculations and a summary report explaining your findings.1.Python Script: To complete the tasks listed below, open the Project Two Jupyter Notebook link in the Assignment Information module. Your project contains the NBA data set and a Jupyter Notebook with your Python scripts. In the notebook, you will find step-by-step instructions and code blocks that will help you complete the following tasks:oHypothesis tests for a population parameter§Hypothesis tests for a population mean§Hypothesis test for a population proportionoHypothesis test for the difference between two population parameters§Hypothesis test for difference between two population means2.Summary Report: Once you have completed all the steps in your Python script, you will create a summary report to present your findings. Use the provided template to create your report. You must complete each of the following sections:oIntroduction: Set the context for your scenario and the analyses you will be performing.oHypothesis tests for the population mean: Discuss all steps of the hypothesis tests and interpret your results.oHypothesis test for the population proportion: Discuss all steps of the hypothesis test and interpret your results.oHypothesis test for the difference between two population means: Discuss all steps of the hypothesis test and interpret your results.oConclusion: Summarize your findings and explain their practical implications.What to SubmitTo complete this project, you must submit the following:Python ScriptYour Jupyter Notebook Python script contains all the statistical analyses you completed for this project. You downloaded your work as an HTML file. Review the file to make sure that every step and all your outputs are included. Submit the HTML file as part of your submission. Review the Jupyter Notebook in Codio Tutorial in the Supporting Materials section if you need help.Summary ReportUse the provided template to create your summary report. The template contains guiding questions to help you complete each section. Be sure to remove these questions before submitting your report. Your summary report should be submitted as a 3- to 5-page Microsoft Word document. It should include an APA-style cover page and APA citations for any sources used. Use double spacing, 12-point Times New Roman font, and one-inch margins.
5 pages
Tutor 1 1
Submission instructions: compute and handwrite solutions submit all work/setup which 1a-c. Suppose we have a new type of M ...
Tutor 1 1
Submission instructions: compute and handwrite solutions submit all work/setup which 1a-c. Suppose we have a new type of MBS to accommodate the ...
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Florida National University Statistics in Health Care Paper
Students will critically analyze the readings from Chapter 3 and 4 in your textbook. This assignment is designed to help y ...
Florida National University Statistics in Health Care Paper
Students will critically analyze the readings from Chapter 3 and 4 in your textbook. This assignment is designed to help you review, critique, and apply the readings to your Health Care setting as well as become the foundation for all of your remaining assignments. You need to read the article (in the additional weekly reading resources localize in the Syllabus and also in the Lectures link) assigned for week 2 and develop a 2-3-page paper reflecting your understanding and ability to apply the readings to your Health Care Setting. Each paper must be typewritten with 12-point font and double-spaced with standard margins. Follow APA style 7th edition format when referring to the selected articles and include a reference page. EACH PAPER SHOULD INCLUDE THE FOLLOWING: 1. Introduction (25%) Provide a brief synopsis of the meaning (not a description) of each Chapter and articles you read, in your own words. 2. Your Critique (50%) What is your reaction to the content of the articles? What did you learn about Prevalence, Incidence and the relationships between them? What did you learn and how you can apply Ordinal and Categorical Variables? Did these Chapter and articles change your thoughts about comparing the extent of Disease between groups? If so, how? If not, what remained the same? 3. Conclusion (15%) Briefly summarize your thoughts & conclusion to your critique of the articles and Chapter you read.How did these articles and Chapters impact your thoughts on quantifying the extent of disease and summarizing Data Collected in the sample? Evaluation will be based on how clearly you respond to the above, in particular: a) The clarity with which you critique the articles; b) The depth, scope, and organization of your paper; and, c) Your conclusions, including a description of the impact of these articles and Chapters on any Health Care Setting.
The graph of a quadratic inequality is shown below. Use the graph to find the solutions to the inequality in terms of x.
The graph of a quadratic inequality is shown below. Use the graph to find the solutions to the inequality in terms of x.A. ...
The graph of a quadratic inequality is shown below. Use the graph to find the solutions to the inequality in terms of x.
The graph of a quadratic inequality is shown below. Use the graph to find the solutions to the inequality in terms of x.A. x ≤ -2 or x ≥ 1B. x < 2 or x > 1C. -2 ≤ x ≤ 1D. -2 < x < 1
MATH 534 KGS Wk 6 Regression & Correlation Simple Linear Regression Analysis Essay
Final Project: Regression and Correlation Analysis Use the dependent variable (labeled Y) and one of the
independ ...
MATH 534 KGS Wk 6 Regression & Correlation Simple Linear Regression Analysis Essay
Final Project: Regression and Correlation Analysis Use the dependent variable (labeled Y) and one of the
independent variables (labeled X1, X2, and X3) in the data file. Select
and use one independent variable throughout this analysis. Use Excel to
perform the regression and correlation analysis to answer the following.
The week 6 spreadsheet can be helpful in this work.Generate a scatterplot for the specified dependent variable (Y) and
the selected independent variable (X), including the graph of the "best
fit" line. Interpret.Determine the equation of the "best fit" line, which describes the
relationship between the dependent variable and the selected independent
variable.Determine the correlation coefficient. Interpret.Determine the coefficient of determination. Interpret.Test the utility of this regression model by completing a hypothesis
test of b=0 using α=0.10. Interpret results, including the p-value.Based on the findings in steps 1-5, analyze the ability of the independent variable to predict the dependent variable.Compute the confidence interval for b, using a 95% confidence level. Interpret this interval.Compute the 99% confidence interval for the dependent variable, for a
selected value of the independent variable. Each student can choose a
value to use for the independent variable (use same value in the next
step). Interpret this interval.Using the same chosen value for part (8), estimate the 99%
prediction interval for the dependent variable. Interpret this interval.What can be said about the value of the dependent variable for
values of the independent variable that are outside the range of the
sample values? Explain.Describe a business decision that could be made based on the results
of this analysis. In other words, how might the business operations
change based on these statistical results.All DeVry University policies are in effect, including the plagiarism policy.Final Project report is due by the end of Week 7.Final Project is worth 130 total points. See grading rubric below.Summarize your results from Steps 1-11 in a 3-page report.
The report should explain and interpret the results in ways that are
understandable to someone who does not know statistics.Submission: The Word document, summary report should be
submitted for questions 1-11. The Excel output can be included as an
appendix, if needed.Format for report:Summary ReportSteps 1-11 addressed with appropriate output, graphs and interpretations. Be sure to number each step 1-11.
QNT275 DeVry University Calculating Binomial Probabilities
Statistical Concepts: ProbabilityBinomial Probability Distribution Calculating Binomial Probabilities NOTE:For ...
QNT275 DeVry University Calculating Binomial Probabilities
Statistical Concepts: ProbabilityBinomial Probability Distribution Calculating Binomial Probabilities NOTE:For question 1, you will be using the same data file your instructor gave you for the Week 2 Lab. Using the data file from your instructor (same one you used for the Week 2 Lab), calculate descriptive statistics for the variable (Coin) where each of the thirty-five students in the sample flipped a coin 10 times. Round your answers to three decimal places and type the mean and the standard deviation in the grey area below.Create scatter plots for the binomial distribution when p=0.50, p=0.25, and p=0.75 (see directions above).Paste the three scatter plots in the grey area below. List the probability value for each possibility in the binomial experiment calculated at the beginning of this lab, which was calculated with the probability of a success being ½. (Complete sentences not necessary; round your answers to three decimal places.) Give the probability for the following based on the calculations in question 3 above, with the probability of a success being ½. (Complete sentences not necessary; round your answers to three decimal places.) Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ½ and n = 10. Either show your work or explain how your answer was calculated. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¼ and n = 10. Write a comparison of these statistics to those from question 5 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = Calculate (by hand) the mean and standard deviation for the binomial distribution with the probability of a success being ¾ and n = 10. Write a comparison of these statistics to those from question 6 in a short paragraph of several complete sentences. Use these formulas to do the hand calculations: Mean = np, Standard Deviation = Using all four of the properties of a Binomial experiment (see page 201 in the textbook) explain in a short paragraph of several complete sentences why the Coin variable from the class survey represents a binomial distribution from a binomial experiment.Compare the mean and standard deviation for the Coin variable (question 1) with those of the mean and standard deviation for the binomial distribution that was calculated by hand in question 5. Explain how they are related in a short paragraph of several complete sentences. Mean: Standard deviation: NOTE:for questions 2-7, you will NOT be using the data file your instructor gave you.Please follow the instructions given in each question. Plotting the Binomial Probabilities For the next part of the lab, open the Week 3 Excel worksheet.This will be used for the next few questions, rather than the data file used for the first question. Click on the “binomial tables” workbookType in n=10 and p=0.5; this simulates ten flips of a coin where x is counting the number of heads that occur throughout the ten flipsCreate a scatter plot, either directly in this spreadsheet (if you are comfortable with those steps), or by using the Week 1 spreadsheet and copying the data from here onto that sheet (x would be the x variable, and P(X=x) would be the y variable.Repeat steps 2 and 3 with n=10 and p=0.25Repeat steps 2 and 3 with n=10 and p=0.75In the end, you will have three scatter plots for the first question below. Calculating Descriptive Statistics Short Answer Writing Assignment – Both the calculated binomial probabilities and the descriptive statistics from the class database will be used to answer the following questions.Round all numeric answers to three decimal places. P(x=0) P(x=6) P(x=1) P(x=7) P(x=2) P(x=8) P(x=3) P(x=9) P(x=4) P(x=10) P(x=5) P(x≥1) P(x<0) P(x>1) P(x≤4) P(4<x ≤7) P(x<4 or x≥7) Mean = np: Standard Deviation = : Mean = np: Standard Deviation = : Comparison: Mean = np: Standard Deviation = : Comparison: NOTE:For questions 8-9, you will use the results of the previous questions. Mean from question #1: Standard deviation from question #1: Mean from question #5: Standard deviation from question #5: Comparison and explanation:
MAT 243 Correlation Coefficient Discussion
PART 1Use the link in the Jupyter Notebook activity to access your Python script. Once you have made your calculations, co ...
MAT 243 Correlation Coefficient Discussion
PART 1Use the link in the Jupyter Notebook activity to access your Python script. Once you have made your calculations, complete this discussion. The script will output answers to the questions given below. You must attach your Python script output as an HTML file and respond to the questions below.In this discussion, you will apply the statistical concepts and techniques covered in this week's reading about correlation coefficient and simple linear regression. A car rental company wants to evaluate the premise that heavier cars are less fuel efficient than lighter cars. In other words, the company expects that fuel efficiency (miles per gallon) and weight of the car (often measured in thousands of pounds) are correlated. Performing this analysis will help the company optimize its business model and charge its customers appropriately.In this discussion, you will work with a cars data set that includes two variables:Miles per gallon (coded as mpg in the data set)Weight of the car (coded as wt in the data set)The random sample will be drawn from a CSV file. This data will be unique to you, and therefore your answers will be unique as well. Run Step 1 in the Python script to generate your unique sample data.In your initial post, address the following items:You created a scatterplot of miles per gallon against weight; check to make sure it was included in your attachment. Does the graph show any trend? If yes, is the trend what you expected? Why or why not? See Step 2 in the Python script.What is the coefficient of correlation between miles per gallon and weight? What is the sign of the correlation coefficient? Does the coefficient of correlation indicate a strong correlation, weak correlation, or no correlation between the two variables? How do you know? See Step 3 in the Python script.Write the simple linear regression equation for miles per gallon as the response variable and weight as the predictor variable. How might the car rental company use this model? See Step 4 in the Python script.What is the slope coefficient? Is this coefficient significant at a 5% level of significance (alpha=0.05)? (Hint: Check the P-value, , for weight in the Python output.) See Step 4 in the Python script.In your follow-up posts to other students, review your peers' calculations and provide some analysis and interpretation:How do their plots and correlation coefficients compare with yours?Would you recommend this regression model to the car rental company? Why or why not?Remember to attach your Python output and respond to all questions in your initial and follow-up posts. Be sure to clearly communicate your ideas using appropriate terminology. Finally, be sure to review the Discussion Rubric to understand how you will be graded on this assignment.PART 2 For this project, you will submit the Python script you used to make your calculations and a summary report explaining your findings.1.Python Script: To complete the tasks listed below, open the Project Two Jupyter Notebook link in the Assignment Information module. Your project contains the NBA data set and a Jupyter Notebook with your Python scripts. In the notebook, you will find step-by-step instructions and code blocks that will help you complete the following tasks:oHypothesis tests for a population parameter§Hypothesis tests for a population mean§Hypothesis test for a population proportionoHypothesis test for the difference between two population parameters§Hypothesis test for difference between two population means2.Summary Report: Once you have completed all the steps in your Python script, you will create a summary report to present your findings. Use the provided template to create your report. You must complete each of the following sections:oIntroduction: Set the context for your scenario and the analyses you will be performing.oHypothesis tests for the population mean: Discuss all steps of the hypothesis tests and interpret your results.oHypothesis test for the population proportion: Discuss all steps of the hypothesis test and interpret your results.oHypothesis test for the difference between two population means: Discuss all steps of the hypothesis test and interpret your results.oConclusion: Summarize your findings and explain their practical implications.What to SubmitTo complete this project, you must submit the following:Python ScriptYour Jupyter Notebook Python script contains all the statistical analyses you completed for this project. You downloaded your work as an HTML file. Review the file to make sure that every step and all your outputs are included. Submit the HTML file as part of your submission. Review the Jupyter Notebook in Codio Tutorial in the Supporting Materials section if you need help.Summary ReportUse the provided template to create your summary report. The template contains guiding questions to help you complete each section. Be sure to remove these questions before submitting your report. Your summary report should be submitted as a 3- to 5-page Microsoft Word document. It should include an APA-style cover page and APA citations for any sources used. Use double spacing, 12-point Times New Roman font, and one-inch margins.
5 pages
Tutor 1 1
Submission instructions: compute and handwrite solutions submit all work/setup which 1a-c. Suppose we have a new type of M ...
Tutor 1 1
Submission instructions: compute and handwrite solutions submit all work/setup which 1a-c. Suppose we have a new type of MBS to accommodate the ...
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