Please answer and show work for following exam review questions

Counting Techniques ALL questions below must be answered. Show ALL step-by-step calculation. Upload this modified Answer Form to the intellipath Unit 8 Submission lesson. Make sure you submit your work in a modified MS Word document; handwritten work will not be accepted. If you need assistance, please contact your course instructor. Part A: Combinations and Permutations 1.Differentiate between permutations and combinations. How are they different? What is the formula for each? (15 points total for Question 1)2.Each state has a standard format for license plates that includes a set number of alphanumeric characters. For this assignment, you can insert a picture of your state’s non-personalized license plate or provide a sample of the format in text. (20 points total for Question 2)a.Determine the number of different license plates that can be created using this format. Assume that a license plate consists of seven alphanumeric characters using numbers (0–9) and capital letters (A–Z). Find how many unique license plates can be printed using all alphanumeric characters only once. b.You and a friend are witnesses of a car accident in your state. But you can only remember a few of the first alphanumeric characters on the license plate. 3.Your community has asked you to help the Young Men's Christian Association (YMCA) sports director organize a season of sports. You need to put together the teams. For the soccer teams, athletes signed up with three different age groups. How many different ways can you organize teams of 10 for each age group? (15 points total for Question 3)For this set of exercises, you will need one standard six-sided dice. If you do not have one, you can use virtual dice: https://www.random.org/dice/ (40 points total for Question 4)a.First, differentiate between odds and probability. b.Reflect on the previous question’s answer outcome. First, convert the fraction to a percent. c.What if someone challenged you to never roll a 3? If you were to roll the dice 18 times, what would be the empirical probability of never getting a three? d.After 18 rolls, what would be the empirical probability of getting a three on at least one of those rolls? Also, list the likelihood scale term from the table above. e.Roll the dice 18 times and keep track of what is rolled in the table below. (2 points)f.Based on your dice rolls, what is the experimental probability of rolling a three, out of 18 rolls? Also, list the likelihood scale term from the table above. How are they different? (5 points) ? Permutation Formula (5 points) ? Combination Formula (5 points) ? Your State’s Name (1 point) Ohio Picture of a License Plate from Your State (or a Sample) (1 point) ? Describe the Rule for Your State’s Non-personalized License Plates (1 point) ? Is this a permutation or combination? Why? (2 points) ? What formula from Question 1 will you use to solve the problem? (1 point) ? Solution: (4 points) ? Show your work here: How many alphanumeric characters do you remember? (1 point) ? (Select a number from 2 to 5) What are the characters at the beginning? (1 point) ? How many license plates start with these alphanumeric characters? (4 points) ? Show your work here: How many license plates have been eliminated? (4 points) ? Show your work: Are these a permutation or combination? Why? (2 points) ? What formula from Question 1 will you use to solve the problem? (1 point) ? How many students signed up for soccer? (1 point) ? (Select a multiple of 10, from 30 to 100) How many kids signed up for Little Tykes under the age of seven? (1 point) ? (Select a multiple of 10, of at least 20) How many kids signed up for Big Kids between the ages 8 and 12? (1 point) ? (Select a multiple of 10, of at least 20) How many kids signed up for Teens between the ages 13 and 18? (1 point) ? (Select a multiple of 10, of at least 20) How many different ways can you create teams of 10 for the Little Tykes grade level? (2 points) ? Show your work here: (2 points) If age levels did not matter, how many different ways can you create teams of 10? (2 points) ? Show your work here: (2 points) Part B: Probabilities and Odds How are odds and probability different? (2 points) ? What is the odds in favor ratio? (3 points) ? What is the probability of an event ratio? (3 points) ? What are the odds of rolling a three? Simplify all fraction answers. (2 points) ? What is the theoretical probability of rolling a three? Simplify all fraction answers. (2 points) ? Percent Probability Theoretical Probability (Rounded to the nearest whole percent.) (2 points) ? Next, given the likelihood scale table above, what term best describes your answer? Likelihood Scale Term (2 points) ? Percent Probability Solution (Rounded to the Nearest Whole Percent) (2 points) ? Likelihood Scale Term (2 points) ? Show your work here: (2 points) Percent Probability Empirical Probability (Rounded to the Nearest Whole Percent) (2 points) ? Likelihood Scale Term (2 points) ? Show your work: (2 points) What do you notice about the answers for parts c and d above? (2 points) ? Roll # Dice Roll # Dice Roll # Dice Roll 1 ? Roll 7 ? Roll 13 ? Roll 2 ? Roll 8 ? Roll 14 ? Roll 3 ? Roll 9 ? Roll 15 ? Roll 4 ? Roll 10 ? Roll 16 ? Roll 5 ? Roll 11 ? Roll 17 ? Roll 6 ? Roll 12 ? Roll 18 ? Percent Probability Experimental Probability (Rounded to the Nearest Whole Percent) (2 points) ? Likelihood Scale Term (2 points) ? Show your work here: (2 points) With regard to the likelihood scale terms for each, how did this differ from both the theoretical and empirical probabilities? (2 points) ?

In this project you will chose a data set that interests you and investigate a possible association between two variables within that data set. This project will give you an opportunity to use StatCrunch to apply the skills and techniques you have learned in this class and to produce a professional report. To produce a successful project you must:Read and follow the instructions carefully.Give yourself sufficient time to work on the project.Write clearly, using appropriate statistical terminology and correct mathematical notation. College-level writing is expected, as is the use of proper grammar.Use StatCrunch to complete all calculations and graphs.Create original work. The following link describes, in detail, plagiarism, fair use and HCC’s academic policy: Fair Use and Academic Honesty (Links to an external site.) Furthermore, this means that students who are repeating the course are expected to create an entirely new project using two new variables of interest.Submit a professional report that is typed and formatted and organized well.SUBMISSION PROTOCOLSubmit your project via Canvas as a PDF or Word file.10% will be deducted for each calendar day the project is submitted after the due date. A project is considered “submitted” when it is available for the professor to grade in Canvas. No credit is given after a submission 5 days late. This assignment utilizes Unicheck, a tool that checks for plagiarism. Unicheck is integrated into the Canvas submission process. All submissions will be compared against a database and receive an originality rating. PROJECT INSTRUCTIONSFor this project you are going to choose one data set from the list below that you find interesting and investigate an association between two variables within that data set. You will then examine the data and write a two page report. In your report you should:Introduce the data set and explain why you chose it.Describe the variables you chose and thoroughly explain what you are investigating. Be sure to define which variable is the explanatory variable and which is the response variable.Using StatCrunch, create an appropriate graph for the association you are investigating and calculate the correlation coefficient and the linear model. Be sure your graph is appropriately labeled and that it includes a title and then copy it into your paper.Report the correlation coefficient.Describe the association you are investigating using correct statistical terminology. Reference your graph and the correlation coefficient, and be sure to note any possible outliers.Report the linear model using correct notation.Interpret the slope and vertical intercept of your model, and discuss the appropriateness of your model.Summarize your findings and draw a conclusion.DATA SETSBelow is a list of data sets - choose one for your project. The links will not work directly, so please follow these directions: In Canvas, click on MyLab and Mastering --> Open My Lab and Mastering --> StatCrunch (on the left) --> Visit the StatCrunch Website --> Open StatCrunch (yellow button at top of page, it will auto login)Then copy/paste a URL below into either the current tab or a new tabTo save your data and work, go to the Data tab and choose SaveTo Re-open your saved file, click on MyLab and Mastering --> Open My Lab and Mastering --> StatCrunch (on the left) --> Visit the StatCrunch Website -->MyStatCrunch (on the right side)-->My Data U.S. CBP Drug Seizure Statistics: https://www.statcrunch.com/app/index.php?dataid=28...This data set summarizes the pounds of drugs seized at ports of entry and between points of entry by the U.S. Customs and Border Protection Agency. https://www.cbp.gov/newsroom/stats/cbp-enforcement...U.S. Presidential Data: https://www.statcrunch.com/app/index.php?dataid=31...This data set contains information on the U.S. Presidents from 1789-2019.Fatal Encounters Updated September 2018: https://www.statcrunch.com/app/index.php?dataid=30...This data set contains information on fatal encounters. Fatal Encounters is a non-profit organization that collects data on police involved deaths. Note: This is a volunteer agency collecting the data from people who are scouring new articles for evidence of these fatal encounters. Thus, this is not a complete population of fatal encounters, only a large sample. https://fatalencounters.org/College Basketball Arenas: https://www.statcrunch.com/app/index.php?dataid=29...This data set contains information on college basketball arenas throughout the country.Marriage vs. the Economy: https://www.statcrunch.com/app/index.php?dataid=28...This data set compares the number of marriages in the last 30 years to several factors of the economy.Medical Costs: https://www.statcrunch.com/app/index.php?dataid=26...This data set contains a variety of personal data in regards to medical costs.MLB August 2019 Batting: https://www.statcrunch.com/app/index.php?dataid=31...This data set contains MLB batter statistics and are year-to-date as of August 18, 2019.Sample College Data: https://www.statcrunch.com/app/index.php?dataid=31...This data set contains a variety of data for colleges and universities in Delaware, DC, Maryland, Pennsylvania, Virginia, and West Virginia. Data is for the year 2011.Fast Food Nutritional Data: https://www.statcrunch.com/app/index.php?dataid=25...This data set contains nutritional information on a variety of fast food items. Data was collected in January 2017 from online sources for each restaurant.Marvel vs. DC at the Box Office: https://www.statcrunch.com/app/index.php?dataid=31...This data set contains information on how the two comic book companies have fared at the box office. Note: The Adjusted column modifies the total Worldwide gross for inflation.NFL Player Data 2016: https://www.statcrunch.com/app/index.php?dataid=27...This data set lists the 2,764 NFL players for all team rosters as of July 22, 2016Car Details 2019 Models: https://www.statcrunch.com/app/index.php?dataid=32...This data set contains information on the 2019 models of widely-known sold cars. MSRP stands for Manufacturer Suggested Retail Price and MPG stands for Miles Per Gallon.Super Heroes: https://www.statcrunch.com/app/index.php?dataid=26...This data set contains various physical characteristics for over 700 fictional comic book superheroes. https://www.kaggle.com/claudiodavi/superhero-setMovie Budgets & Box Office Earnings (Updated Spring 2018): https://www.statcrunch.com/app/index.php?dataid=21...This data comes from the following website that tracks the financial performance of movies: https://www.the-numbers.com/movie/budgets/all; columns each are in millions of dollars COMPLETION CHECKLISTUse the following checklist when proofreading your project.For each aspect below, an excellent report will: IntroductionGive the name of the data set chosen as well as some details describing the data set. (This may require following links or referencing the text)Include a clear justification for why the data set was chosen.Involve two quantitative variables.Clearly and thoroughly describe the variables chosen. (This may require following links or referencing the text)Clearly and correctly assign explanatory and response variables.Thoroughly explain the association being investigated and give a logical justification for why the author believes the association exists.GraphInclude an appropriate scatterplot generated using StatCrunch.Accurately assign and clearly label the axes for the scatterplot.Include an appropriate title for the scatterplot. Include the appropriate correlation coefficient for the association generated using StatCrunch.Include an accurate and thorough description of the association with reference to the graph, correlation coefficient and any outliers. Linear Association ModelInclude an appropriate linear regression model generated using StatCrunch and written using correct notation and typesetting.Give an accurate and detailed interpretation of the slope of the linear regression model.Give an accurate and detailed interpretation of the y-intercept of the linear regression model.Thoroughly discuss the appropriateness of the linear regression model with reference to other aspects of the report.ConclusionIncludes a summary of the findings and a clear conclusion regarding the association.Appear highly professional, be easy to read and comprehend, and use correct statistical vocabulary. ASSISTANCEFor this project, you may consult any resource for general help and advice provided that your computations, explanations, and embedded diagrams are your own work.The Math Center is a drop-in tutoring center for math located in HR230. For more information, click the following link: MaC (Links to an external site.) HOWL, the HCC Online Writing Lab, offers assistance with writing assignments. For more information, click on the following link: HOWL (Links to an external site.) RubricLinear Regression RubricLinear Regression RubricCriteriaRatingsPtsThis criterion is linked to a Learning OutcomeIntroduction: Data SetAn excellent report will give the name of the data set chosen as well as some details describing the data set.2.0 ptsFull CreditName of the data set chosen as well as some details describing the data set.1.0 ptsHalf CreditName of data set is given but no further description or details.0.0 ptsNo CreditData Set chosen is not identified.2.0 ptsThis criterion is linked to a Learning OutcomeIntroduction: Justification for Data SetAn excellent report will include a clear justification for why the author chose the data set.2.0 ptsFull CreditClear and logical justification given.1.0 ptsHalf CreditJustification is overly vague or not logical.0.0 ptsNo CreditNo justification given.2.0 ptsThis criterion is linked to a Learning OutcomeIntroduction: Two Quantitative VariablesAn excellent report will involve two quantitative variables.2.0 ptsFull CreditBoth variables chosen are quantitative.1.0 ptsHalf CreditOnly one of the chosen variables is quantitative.0.0 ptsNo CreditNeither variable chosen is quantitative.2.0 ptsThis criterion is linked to a Learning OutcomeIntroduction: Description of VariablesAn excellent report will include a clear and thorough description of the chosen variables .4.0 ptsFull CreditClear and thorough description of variables given.2.0 ptsHalf CreditDescription of variables is unclear or nondescript.0.0 ptsNo CreditNo description of variables given.4.0 ptsThis criterion is linked to a Learning OutcomeIntroduction: Explanation of InvestigationAn excellent report will include a clear and thorough explanation and justification of the association being investigated.6.0 ptsFull CreditClear and thorough explanation of what is being investigated including logical justification.3.0 ptsHalf CreditDescription of what is being investigated is vague or illogical.0.0 ptsNo CreditDescription of what is being investigated is missing.6.0 ptsThis criterion is linked to a Learning OutcomeIntroduction: Explanatory and Response VariablesAn excellent report will clearly and correctly assign the explanatory and response variables.2.0 ptsFull CreditExplanatory and Response variables are clearly and appropriately assigned.1.0 ptsHalf CreditExplanatory and response variables are assigned incorrectly.0.0 ptsNo CreditIt is not clear which is the explanatory variable and which is the response variable.2.0 ptsThis criterion is linked to a Learning OutcomeGraph: Scatterplot Generated using StatCrunchAn excellent report will include an appropriate scatterplot generated using StatCrunch.6.0 ptsFull CreditReport includes an appropriate scatterplot generated using StatCrunch.3.0 ptsHalf CreditA scatterplot is present but it was not generated using StatCrunch.0.0 ptsNo CreditNo scatterplot given or scatterplot was created by hand.6.0 ptsThis criterion is linked to a Learning OutcomeGraph: Appropriately Assigned AxesAn excellent report will include appropriately assigned and clearly labeled axes for the scatterplot.2.0 ptsFull CreditAxes are appropriately assigned and labeled.1.0 ptsHalf CreditAxes are assigned incorrectly.0.0 ptsNo CreditAxes are not labeled.2.0 ptsThis criterion is linked to a Learning OutcomeGraph: TitleAn excellent report will include an appropriate title for the scatterplot.2.0 ptsFull CreditScatterplot includes an appropriate title.1.0 ptsHalf CreditA title is present but it does not accurately describe the graph.0.0 ptsNo CreditScatterplot does not have a title.2.0 ptsThis criterion is linked to a Learning OutcomeCorrelation CoefficientAn excellent report will include the appropriate correlation coefficient generated using StatCrunch.4.0 ptsFull CreditAppropriate correlation coefficient is generated using StatCrunch and it is clear that the student knows which value outputted by StatCrunch is the correlation coefficient.2.0 ptsHalf CreditStudent includes what was generated by StatCrunch, but it is unclear that they know which value is the correlation coefficient.0.0 ptsNo CreditNo correlation coefficient is given.4.0 ptsThis criterion is linked to a Learning OutcomeDescription of AssociationAn excellent report will include an accurate and thorough description of the association with reference to the graph, the correlation coefficient and any outliers.8.0 ptsFull CreditAn accurate and thorough description of the association is given with references to the scatterplot, the correlation coefficient and any outliers.6.0 ptsPartial CreditDescription of association is correct but there is no reference to either the graph, the correlation coefficient or any outliers.4.0 ptsHalf CreditDescription of association is given but it is partially incomplete or incorrect.2.0 ptsPartial CreditThe description of the association has many errors and does not reference the scatterplot, the correlation coefficient or any outliers.0.0 ptsNo CreditNo description of the association given.8.0 ptsThis criterion is linked to a Learning OutcomeLinear Regression ModelAn excellent report will include an appropriate linear regression model generated using StatCrunch.4.0 ptsFull CreditAppropriate model is generated using StatCrunch and it is clear that the student knows the equation for the model outputted by StatCrunch.2.0 ptsHalf CreditStudent includes what was generated by StatCrunch, but it is unclear that they know what the linear regression model is.0.0 ptsNo CreditNo linear regression model is given.4.0 ptsThis criterion is linked to a Learning OutcomeLinear Regression Model: Correctly TypedAn excellent report includes the linear regression model written using correct notation and typesetting.3.0 ptsFull CreditLinear regression model is correct and written using proper notation.2.0 ptsPartial CreditLinear regression model is correct but not written using proper notation.1.0 ptsPartial CreditLinear regression model is not correct.0.0 ptsNo CreditNo linear regression model is given.3.0 ptsThis criterion is linked to a Learning OutcomeLinear Regression Model: Interpretation of SlopeAn excellent report will include an accurate and detailed interpretation of the slope.2.0 ptsFull CreditInterpretation of the slope of the model is correct and precise.1.0 ptsHalf CreditInterpretation of the slope is vague or has minor errors.0.0 ptsNo CreditInterpretation of slope is missing or completely incorrect.2.0 ptsThis criterion is linked to a Learning OutcomeLinear Regression Model: Interpretation of InterceptAn excellent report will include an accurate and detailed interpretation of the intercept.2.0 ptsFull CreditInterpretation of the intercept of the model is correct and precise.1.0 ptsHalf CreditInterpretation of the intercept is vague or has minor errors.0.0 ptsNo CreditInterpretation of the intercept is missing or completely incorrect.2.0 ptsThis criterion is linked to a Learning OutcomeLinear Regression Model: Appropriateness of ModelAn excellent report will include a detailed and thorough discussion of the linear regression model with reference to other aspects of the report.4.0 ptsFull CreditDiscussion of appropriateness of linear regression model is detailed and thorough and references other aspects of the report.2.0 ptsHalf CreditDiscussion is vague and/or doesn't reference other aspects of report.0.0 ptsNo CreditNo discussion of the appropriateness of the model is given.4.0 ptsThis criterion is linked to a Learning OutcomeConclusion: Summary of FindingsAn excellent report includes an accurate summary of the findings.2.0 ptsFull CreditA sufficient summary of the findings is given.1.0 ptsHalf CreditThe summary of findings is incorrect or incomplete.0.0 ptsNo CreditNo summary is given.2.0 ptsThis criterion is linked to a Learning OutcomeConclusion: Final ConclusionAn excellent report includes a clear and accurate final conclusion on the association being investigated.4.0 ptsFull CreditFinal conclusion on the association being investigated is clear and accurate.2.0 ptsHalf CreditFinal conclusion is incomplete or partially incorrect.0.0 ptsNo CreditNo final conclusion is given.4.0 ptsThis criterion is linked to a Learning OutcomeProfessionalismAn excellent report is highly professional in appearance, easy to read and comprehend, and uses correct statistical vocabulary.4.0 ptsFull CreditReport is highly professional in appearance, easy to read and comprehend, and uses correct statistical vocabulary.2.0 ptsHalf CreditReport demonstrates some professionalism but contains distracting errors or problems with formatting, organization, vocabulary or grammar.0.0 ptsNo CreditReport is severely lacking in professionalism and/or errors or problems with formatting, organization, vocabulary or grammar make report far too difficult to read.4.0 ptsTotal Points: 65.0