EXAM Answer all questions in the exam document embedded below. After you completed your exam, scan your pages into a single PDF, name it midterm_Student Name (example: midterm_JohnSmith).  Before uploading, verify your file has all the pages you need to submit. Upload it by clicking on “Choose a File” button in “Question 1” below. You are only allowed to upload one file to a question. Then click “Submit Quiz”. You may get a warning saying that you have some unanswered questions if you do not use optional file upload sections, click OK to submit anyway. View exam document here. Use double-sided arrow icon on the tool bar below to preview it in full screen mode. You can also download it by clicking on the download icon to the right of the document and open it on your computer. midterm – 2025.pdf

What R function is used to calculate the probability of exactly k events occurring in a Poisson distribution?

If, on average, 8 customers arrive at a store every hour, what is the value of λ for a Poisson distribution modeling this situation?

Based on the given R output from the str(data) function, which of the following statements is correct?

Which of the following best explains the importance of conditional probability in real-world applications?

A bag contains 5 red, 4 blue, and 3 green balls. If a ball is randomly selected, what is the probability that it is not blue?

In a Bernoulli trial, the probability of failure is denoted by:

A student scores 75 on a test with a mean of 60 and a standard deviation of 5. What is the student’s Z-score?

Which R function is used to determine the length of a vector?

What is the value of 5! (5 factorial)?