ALY_6000_Project_6

Project 6 ALY 6000 Project Instructions For your final project, you will use R to solve problems about probability distributions. Specifically, you will make use of the d, p, q, and r functions built into R for working with probability distributions. In most cases, you will need to determine the type of probability distribution that is described and use R to determine a numerical answer. Note: Utilize the file project6_tests.R with the code below to run a series of tests (not comprehensive) on your code. Any failed test signals that something is wrong with the results or that you have not utilized the specified variable names. p_load (testthat) #testthat::test_file("project6_tests.R") Questions not checked by the test file will be graded manually after the due date. When completed you will submit your work as LastName-FirstName-Project6.Rmd and Lastname_Project6_Report.pdf. Problems Analyzing a baseball probability distribution In the next group of problems, consider the Boston Red Sox playing a stretch of seven games, where the probability of winning a game is 0.65 and an outcome is the number of wins during those seven games. 1. What is the probability that the Red Sox will win exactly 5 games ( prob1_result )?

2. Use data.frame() or tibble() to create a dataframe or tibble with each possible outcome and the probability of that outcome. Name your columns wins and probability ( prob2_result ). 3. What is the probability that the Red Sox will win fewer than 5 games ( prob3_result )? 4. What is the probability that the Red Sox will win between 3 and 5 games inclusively ( prob4_result )? 5. What is the probability of the Red Sox winning more than 4 games ( prob5_result )? 6. What is the theoretical expected value of the number of wins for the Red Sox in a 7- game series ( prob6_result )? 7. What is the theoretical variance of the number of wins for the Red Sox in a 7- game series ( prob7_result )? 8. Generate 1,000 random values for the number of wins by the Red Sox in a 7- game series. Use set.seed(10) before generating the random values. 9. Compute the sample mean of the 1,000 random values ( prob9_result ). 10. Compute the sample variance of the 1,000 random values ( prob10_result ). Analyzing calls in a call center The number of calls received each hour at a call center follows a Poisson distribution averaging seven calls per employee per hour. 11. What is the probability that an employee will receive exactly 6 calls in the next hour ( prob11_result )? 12. What is the probability that an employee will receive 40 or fewer calls in the next 8 hours ( prob12_result )? 13. Assuming that there are 5 employees working eight-hour shifts, what is the probability that they will meet the quota of 275 or more calls during the shift ( prob13_result )? 14. If one employee is sick, what is the probability that the remaining team will still meet the quota of 275 or more calls during their shift ( prob14_result )? 15. For a single employee working an 8-hour shift, how many calls are necessary for the day to be considered in the top 10% of days volume-wise ( prob15_result )? 16. Generate 1,000 random values for the number of calls for a single employee during an 8-hour shift. Use a set.seed(15) before creating values. 17. Compute the sample mean of the 1,000 random values ( prob17_result ).

30. Write up your results about the penguins in an executive summary called LastName_Project6_Report.pdf. When you are satisfied with your solution, submit two (2) files in Canvas: 1. Your R Markdown file, named LastName-FirstName-Project6.Rmd . 2. A PDF of your four-page report titled Lastname_Project6_Report.pdf . Your report should contain the following information, formatted as specified: Title Page Include your name, assignment title, and submission date. Introduction and Key Findings Include an overview of the assignment and any findings. Conclusion/Recommendations Include evidence-based recommendations and visualizations or direct presentation of tabular data. Works Cited Include all sources, including YouTube videos, instruction materials, Google search results, and texts that informed your study of statistics and R. Your report should be as concise as possible while maintaining fluency. Your key findings will be strongest if supported by visualizations or direct presentation of tabular data. Your summary must adhere to APA guidelines, including page numbers on each page (including the title page) in the upper right corner. See the following examples for title pages , citations , and general APA formatting . Congratulations on completing Project 6!