ALY_6000_Project_6

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Northeastern University *

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6000

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Statistics

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Apr 3, 2024

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pdf

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4

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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. Setting up Your Project When working in RStudio, be careful with cloud drives. RStudio does not always play well with cloud drives’ longer file path names. You w ill be best served by using a local drive whenever possible until you are comfortable troubleshooting technical issues. 1. Create a new project called “Lastname - Project6”. 2. Create an R Script file within your project called “Lastname - Project6.R”. 3. Include your name, the date, and the class in a comment as the first line of the script. 4. Include any script initialization code and library loading. Testing Your Solution You can evaluate your project using the project5_tests.R test file. This will only work if you store results in the exact variable names specified in bold and in parentheses at the end of the problem. 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 .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. Create a data.frame 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 ).
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