Instructions: Answer each question in the space provided. If the question asks you to show work or provide an explanation along with your answer you must include the work and/or explanation or no credit will be awarded. [There are 40 questions. Each one is worth 2.5 points.] Questions 1 - 3 refer to the histogram below which shows the final exam scores of a sample of students. Questions 1 - 6. Write your answer and explanation in space provided. Answer and Explanation 1. What percentage of the students scored below 70? 2. Is 60 a possible value of the median for the exam scores? 3. What is the shape of this distribution? Questions 4 - 6 refer to the boxplots below which display midterm exam scores for all students in two different sections of the same course. [Note. These questions are not connected to Q 1-3.] For each of the following questions, write the letter of your answer AND explain why you think that is the correct answer (Answers with no explanation will not receive credit) A) Section A B) Section B C) Both sections are about equal D) It is impossible to tell Answer and Explanation 4. Which section has more students? 5. Which section has a greater percentage of students with scores at or above 80? 6. Which section has a greater percentage of students with scores at or above 55? Questions 7 - 10: In addition to answering the following questions, show your work and/or explain how you arrived at your answer. [If you're not sure what is required, look at the answers to Week 8's homework to get an idea of what to include in your answer.] 7. At a large department store, the average number of years of employment for a cashier is 3.6 with a standard deviation of 1.4 years, and the distribution is approximately normal. If an employee is picked at random, what is the probability that the employee has worked at the store for more than 5 years? 8. The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 22 minutes and a standard deviation of 3 minutes. The probability is ________ that a product is assembled in between 15 and 19 minutes. 9. The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 22 minutes and a standard deviation of 3 minutes. According to the Standard Deviation Rule, almost all (99.7%) of the products will be completed between _____minutes and _____ minutes. 10. The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 22 minutes and a standard deviation of 3 minutes. The probability is .33 that a product is completed in less than _____ minutes. Questions 11 - 20: Use the attached data set bbdata16s.xls to answer these questions. Give your answers with at least 2 decimal places. (Be careful to follow the rules of rounding.) Questions 11 - 15: For the variable Average Ticket Price (Average Ticket$), use Excel to find the following: 11. median 12. mean 13. sample standard deviation 14. What is the shape of this distribution? Give a piece of evidence based on the statistics above to support your answer. 15. According to the IQR rule, are there any outliers? Explain how you arrived at your answer. If there are any outliers, identify the team(s). Questions 16 - 20: A sports writer knows that fans will generally pay more to see a winning team and wants to see if it is possible to use the number of wins in a season (Wins) to predict the average ticket price. Use the data to create a scatterplot, add a trendline and request whatever additional information you need to answer the following questions: 16. Describe the overall pattern of the relationship between number of wins and average ticket price. 17. What is the equation for the least squares regression line for the relationship between number of wins and average ticket price? 18. Predict the average ticket price for a team that wins 75 games. 19. For every additional win a team gets, their average ticket price would be expected to _______ by ______. 20. What is the correlation between wins and average ticket price? (numerical answer required) Questions 21 - 40. No work or explanation required unless specifically asked for. 21. What type of sampling is represented by the following scenario? Citibank wants to survey its employees. 25 branches are randomly selected and all of the employees in those branches are given the survey. 22. What type of sampling is represented by the following scenario? From a list of all Walmart employees, the research staff divides the list into full-timers and part-timers and randomly selects a sample of 500 from each group. 23. What type of sampling is represented by the following scenario? A researcher goes to a large company's office building and interviews all employees who are in the lunchroom between 12 and 2 pm. 24. An appliance store surveyed 300 dishwasher customers to see if they were satisfied with their purchase. 80 had bought a Kitchenaid dishwasher and the rest had bought a Maytag dishwasher. 64 of the 240 customers who said they were satisfied had bought a Kitchenaid. Fill in the two-by-two table in the Answer column. Use the following key for the variables: K = Kitchenaid M = Maytag S = Satisfied NS = Not Satisfied 25. How many variables are in the table you constructed in the previous question? Name them. 26 Use the information in Q 24. What is the probability a customer bought a Maytag or is satisfied? 27. Use the information in Q 24. If a customer bought a Maytag, what is the probability the customer is not satisfied? 28. In Q 24, are the variables independent? Support your answer using appropriate numbers from your table to illustrate one of the guidelines for determining if variables are independent. 29. At a different company, 700 of the 2000 employees are male. If two employees are randomly selected, what is the probability that they are the same gender? 30. A student is taking a very short multiple-choice quiz in which each question has 4 choices - - A, B, C, D. The student hasn't studied so he randomly selects an answer for each of the 3 questions. What is the probability that he gets all 3 questions correct? 31. What is the probability that the student in the previous question gets at least one answer correct? 32. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.3. Assuming that the two events are independent, the probability that the cost is kept within budget or that the campaign will increase sales is ______. 33. Two CUNY students are randomly selected. Let A represent the event "the first student lives in Queens." Let B represent the event "the second student lives in Queens." Are the events A and B disjoint? Explain your answer. 34. Referring to the question above, are the events A and B independent? Explain your answer. 35. The manager of a marketing department wants to select 3 employees to serve on a weekly council. He is using Excel. In the spreadsheet below, the first column contains an alphabetical list of all employees in the department. In the second column, the manager has just generated a list of random numbers. a) What should the manager do next? b) Who will be the 3 employees selected? 36. Imagine a spinner with 3 colors - - Red, White, Blue - - and the colors are the same size. Someone plans to spin the pointer 2 times, but will stop spinning if the pointer lands on Blue. List all the possible outcomes of this random experiment. [Use the letters R, W, B] 37. Three of the four following statements contain a mistake. Identify the statement which could be true and explain the mistake in each of the others. A) The correlation between age and color preference is 0.51. B) The correlation between the pounds of fertilizer used and the height of bean plants is .44. C) In catfish, there is a high correlation (1.05) between their length and their age. D) There is a correlation of 0.23 between religion and political party affiliation. 38. A survey of banks revealed the following distribution for the interest rate being charged on a home loan. Interest Rate Probability 4.90% to 4.99% 0.12 5.00% to 5.09% 0.23 5.10% to 5.19% 0.24 5.20% to 5.29% 0.35 5.30% and above 0.06 If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 5.19%? 39. Questions 39 and 40 are based on the following table: Job Application Outcome Applicant Age Younger than 40 40 or older Total Hired 79 27 106 Not hired 1165 189 1354 Total 1244 216 1460 For the table above, would it be more appropriate to calculate conditional row percentages or conditional column percentages? Explain your answer. 40. Job Application Outcome Applicant Age Younger than 40 40 or older Total Hired Not hired Fill in the table with the appropriate percentages. Total