Assignment Task
Business Statistics
Directions: Please answer each of the following questions independently. Remember, if you do work with some of your classmates while setting up these problems, your explanations should all be your own work – I do not want people to be handing in assignments that are exactly the same. Other than that, please feel free to use any resource available to you. These include: your textbook, the PowerPoints from class, practice resources on the Person website, and of course, me. I am always available via email, and we will have two more class sessions (and I will have two more in-person office hours) for you to bring any questions you might like to discuss in person. Your completed assignment will be due on Sunday, November 14th by 11:59 pm. Feel free to handwrite or hand-draw your answers where applicable (you can also type answers out in a Word document if that is preferable), but you will certainly need to use Excel to complete a number of these problems also. Please scan and upload your work to Canvas (I will provide a link to do so when we get closer to the due date). Canvas should allow you to upload multiple documents as needed, so if you end up having some answers in a Word document and other answers in a handwritten document that you scan, that will be perfectly fine. According to the American Marketing Association, in one particular month, 18% of the users on social media were between 25 and 34 years old. If a random sample of 9 social media users was selected, determine each of the following (please round your answers to four decimal places as needed).
- What is the probability that exactly five social media users in this sample were between 25 and 34 years old?
- What is the probability that fewer than four social media users in this sample were between 25 and 34 years old?
- What is the probability that eight or more social media users in this sample were between 25 and 34 years old?
- What are the mean and standard deviation for this probability distribution? What would it mean if the standard deviation were to increase for this distribution?The faculty members in a particular department at a state university consist of 11 full-time faculty members and 4 part-time faculty lecturers. A committee of 5 faculty members is to be created at random from the members of this department. Determine each of the following (please round your answers to four decimal places as needed).
- If we define a “success” in this scenario to be selecting a full-time faculty member to be on the committee, what are the mean and standard deviation of this probability distribution?
- What is the probability that the committee will consist of exactly three full-time faculty members and exactly two part-time faculty lecturers?
- What is the probability that the committee will consist of exactly two full-time faculty members and exactly three part-time faculty lecturers?
- What is the probability that the committee ends up consisting entirely of full-time faculty members?
- In a few short sentences, explain why the distribution used to model this scenario is more appropriate than the other available options.Suppose that the time between hits on an e-commerce website follows the exponential distribution with a mean time of 2.9 minutes. Determine each of the following (please round your answers to four decimal places as needed).
- What is the probability that the next hit on the website will occur within the next 4 minutes?
- What is the probability that the next hit on the website will take place between 3 and 7 minutes from now?
- What is the probability that it will take more than 5 minutes for the next hit on the website to occur?
- Calculate the standard deviation for this distribution, and offer an interpretation of its meaning.
- How would the shape of the exponential distribution be impacted if the mean time between hits on the website were to increase?
- (20 points) Much of a yearly basketball tournament takes place during the workweek. According to a? survey, 30% of employed adults who plan to watch at least one tournament game say that they have watched the yearly basketball tournament at the office. A random sample of 40 employed adults who plan to watch at least one tournament game was selected. Use the normal approximation to the binomial distribution to determine each of the following (please round your answers to four decimal places as needed).
- Calculate the mean and standard deviation for this distribution.
- What is the probability that more than 16 adults from this sample will watch the tournament at work?
- What is the probability that exactly 12 adults from this sample will watch the tournament at work?
- What is the probability that 8, 9, 10, 11, or 12 adults from this sample will watch the tournament at work?
- What is the probability that fewer than 19 adults from this sample will watch the tournament at work?
- The first draft of a 300-page manuscript has 24 typos that are spread randomly across the pages. Assume that the number of typos per page follows a Poisson distribution, and determine each of the following (please round your answers to four decimal places as needed).
- What is the probability that there is exactly one typo in the first 10 pages?
- What is the probability that there is exactly one typo in the first 20 pages?
- What is the probability that there are exactly four typos in the first 80 pages?
- What is the probability that there are exactly thirteen typos in the first 100 pages?
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