MBA 6300 online Homework Assignment #1 Statistics and Probability and Statistical Process Control Instructions: After the student calculates the answers to this homework he/she must submit the answers by placing them in the Assignment # _ Submittal Link in Bb by midnight of the date shown in the Course Roadmap and Syllabus. The Instructor does not allow late submissions therefore a score of zero (0) will be recorded for the assignment if submitted after midnight Eastern Time of the due date. Solutions for the assignment will be released in Bb the morning after the due date for access by students. Total points for the assignment is 144. Note: There is no partial credit given; either the answer is correct or incorrect. After you have submitted your answers in the Assignment #_ Submission Link, upload the Excel file containing your answers and calculations into the Home Work #_ Supporting Documentation Submission link prior to the due date and time. As stated in the syllabus a score of zero will be awarded for the assignment if this Excel file is not submitted. Scenario #1: The head of the chemistry department at a local university has tasked a student teaching assistant to prepare a variety of statistics pertaining to the final course grades earned by students who have completed the university's CHEM 103 course during the past ten years. These statistics will be used as a basis for predicting the potential performance of future students who enroll in the course. A total of 1,125 students have completed the course during the past ten years. Rather than trying to have the teaching assistant collect and analyze data for all 1,125 students, the department head has agreed to allow the teaching assistant to prepare the necessary statistics using a small random sample consisting of 25 students who completed the course during the past ten years. The following table summarizes the final course grades earned by the 25 randomly selected students. Student No. 1 2 3 4 5 6 7 8 9 10 11 12 13 Course Grade 83.17 82.31 90.18 93.63 92.38 96.06 83.75 85.17 86.67 94.27 83.11 82.16 89.48 Student No. 14 15 16 17 18 19 20 21 22 23 24 25 Dr. Mike's MBA 6300 HW# 1 Page 1 Course Grade 86.76 88.69 86.89 88.57 96.93 86.48 92.15 92.32 78.70 92.67 74.56 78.48 Data: For the purposes of this assignment, assume that: (1) the small sample consisting of 25 students is truly representative of the population of 1,125 students from which it was drawn; and (2) the 1,125 students who have completed the course during the past ten years constitute a truly representative sample of all future students who will eventually enroll in the course. Based upon these assumptions, use the sample data provided in the preceding table to answer the following questions. This HW is worth a total of 144 total points. The points for each question may vary. Question 1. What is the predicted range for the mean grade for an average future student enrolling in the CHEM 103 course? (3 points) Range = 96.93 - 74.56 = 22.37 Question 2. What is the predicted mean grade for an average future student enrolling in the CHEM 103 course? (3 points) Mean = x/n Mean = 2185.54/25 = 87.42 Question 3. What is the predicted median grade for an average future student enrolling in the CHEM 103 course? (3 points) Median = 13th point in the data set = 86.89 Question 4. What is the predicted standard error of the mean grade for an average future student enrolling in the CHEM 103 course? (3 points) Standard error = s/n = 5.76/25 = 1.152 Question 5. Assuming the level of confidence for the interval estimate is not specified, what is the predicted interval estimate for the mean grade for an average future student enrolling in the CHEM 103 course? (4 points) Assumption: 2 standard deviations from the mean. xx t*s/n 87.42 2*1.15 87.42 2.30 85.12, 89.72 Dr. Mike's MBA 6300 HW# 1 Page 2 Question 6. Assuming that a 99% level of confidence for the interval estimate is desired, using the sample data, what is the predicted interval estimate for the mean grade for an average future student enrolling in the CHEM 103 course? (4 points) z (0.01/2) = z (0.005) = 2.576 99% confidence interval xx t*s/n 87.42 2.576*1.15 87.42 2.96 84.46, 90.38 Question 7. Using the sample data, calculate the predicted variance for the grades for average future students enrolling in the CHEM 103 course? (4 points) Variance = v(x) v(x) = (x - xx)/ (n - 1) = 796.37/24 = 33.18 Question 8. Using the sample data, calculate the predicted standard deviation for the grades for average future students enrolling in the CHEM 103 course? (4 points) Standard deviation= s s= (x - xx )/ (n - 1) s = 796.37/24 s = 5.76 Scenario #2 Data: 45 students in two sections of a college Physics 101 course recently took a mid-term exam. 12 students earned an A, 9 students earned a B, 8 students earned a C, 8 students earned a D and 8 students earned an F on the exam. The students were queried regarding the number of hours they had devoted to studying for the exam, 10 of the students who earned an A, 6 of the students who earned a B, 6 of the students who earned a C, 4 of the students who earned a D, and 2 of the students who earned an F reported that they had devoted more than 8 hours to studying for the exam. The remaining students reported that they had devoted no more than 8 hours to studying for the exam. Question 9. What is the probability of a randomly selected student having earned an A on the exam? (3 points) P (A) = 12/(12 + 9 + 8 + 8 + 8) = 12/45 = 0.267 Dr. Mike's MBA 6300 HW# 1 Page 3 Question 10. What is the probability of a randomly selected student having earned a B on the exam? (3 points) P (B) = 9/(12 + 9 + 8 + 8 + 8) = 9/45 = 0.20 Question 11. What is the probability of a randomly selected student having devoted no more than 8 hours to studying for the exam? (3 points) P (<8 hours) = [45 - (10+6+6+4+2)]>8 hrs) = (2/45)/ [10+6+6+4+2)/45] = 0.07 Question 14. What is the probability of a randomly selected student having earned an A or a B on the exam given they devoted more than 8 hours to studying for the exam? (3 points) P (A or B>8 hrs) = 37/45 = 0.82 Data: Scores for a certain exam follow a normal distribution with a mean of 82.54 and a standard deviation of 3.15. Answer questions 15 and 16 using the preceding information. Question 15. What is the standard Z-score associated with a score of 86.45? (3 points) = (86.45 - 82.54)/3.15 = 1.24 Question 16. What is the probability that a randomly selected student's score will fall between a standard Z-score of -1.45 and a standard Z-score of 1.88? (3 points) Data: The mean time required to complete a certain type of construction project is 61 weeks with a standard deviation of 4.25 weeks. Answer questions 17-20 using the preceding information and modeling this situation as a normal distribution. Dr. Mike's MBA 6300 HW# 1 Page 4 xx = 61 s = 4.25 Question 17. What is the probability of the completing the project in no more than 58 weeks? (3 points) Z score = .705 P(x<58) = .2404 Question 18. What is the probability of the completing the project in more than 62 weeks? (3 points) Z score = .235 P(x>62) = .4707 Question 19. What is the probability of completing the project between 58 weeks and 65 weeks? (3 points) P(58