MBA 6300 online Homework Assignment #1 | Complete Solution

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 (provided you by the Instructor) 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: 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. Course Grade  Student No. Course Grade
1 83.17  14 86.76
2 82.31  15 78.55
3 90.18  16 86.89
4 93.63  17 88.57
5 89.56  18 96.93
6 96.06  19 86.48
7 83.75  20 97.12
8 85.17  21 92.32
9 86.67  22 78.70
10 88.16  23 92.67
11 83.11  24 74.56
12 82.16  25 78.48
13 89.48   

Scenario 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 100 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)

Question 2. What is the predicted mean grade for an average future student enrolling in the CHEM 103 course? (3 points)

Question 3. What is the predicted median grade for an average future student enrolling in the CHEM 103 course? (3 points)

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)

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)

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)

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)

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)

Scenario 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.  9 of the students who earned an A, 6 of the students who earned a B, 5 of the students who earned a C, 2 of the students who earned a D, and 1 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)

Question 10. What is the probability of a randomly selected student having earned a B on the exam? (3 points)

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)

Question 12. What is the probability of a randomly selected student having earned an A on the exam given they devoted no more than 8 hours to studying for the exam? (3 points)

Question 13. What is the probability of a randomly selected student having earned an F on the exam given they devoted more than 8 hours to studying for the exam? (3 points)

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)

Scenario 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 88.12? (3 points)

Question 16. What is the probability that a randomly selected student’s score will fall between a standard Z-score of -1.65 and a standard Z-score of 1.88? (3 points)

Scenario Data: The mean time required to complete a certain type of construction project is 61 weeks with a standard deviation of 4.15 weeks.  Answer questions 17 - 20 using the preceding information and modeling this situation as a normal distribution.

Question 17. What is the probability of the completing the project in no more than 58 weeks? (3 points)

Question 18. What is the probability of the completing the project in more than 62 weeks? (3 points)

Question 19. What is the probability of completing the project between 58 weeks and 65 weeks?  (3 points)

Question 20. What is the probability of completing the project within plus or minus one standard deviation of the mean? (3 points)

THE REMAINING QUESTIONS REFER TO STATISTICAL PROCESS CONTROL

Scenario: A manufacturer of automobile glass employs a constant quality control technique where the thickness of glass is checked periodically by taking a sample of 5 units and measuring the thickness. The results of one shift’s quality control inspections are shown in the table below.

Sample Thickness  Sample Thickness
1 4, 3, 4, 2, 4  11 1, 6, 4, 4, 2
2 5, 3, 5, 4, 2  12 3, 3, 4, 5, 4
3 3, 3, 3, 3, 4  13 6, 3, 5, 5, 7
4 4, 5, 5, 4, 5  14 3, 2, 5, 4, 2
5 7, 1, 1, 6, 1  15 3, 3, 3, 2, 1
6 4, 5, 2, 5, 4  16 4, 4, 4, 5, 3
7 3, 5, 4, 4, 5  17 5, 3, 4, 4, 3
8 2, 4, 4, 4, 3  18 4, 4, 5, 3, 3
9 5, 4, 3, 2, 5  19 6, 4, 3, 3, 3
10 4, 4, 4, 4, 4  20 4, 4, 3, 5, 4

Question 21: Using the data contained in the scenario calculate the Upper Control Limit for an X-bar chart that reflect a 99.7% confidence level. (2.5 points)

Question 22: Using the data contained in the scenario calculate the Lower Control Limit for an X-bar chart that reflect a 99.7% confidence level. (2.5 points)

Question 23: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an X-bar chart, which samples are out of control? (5 points)

Question 24: Using the data contained in the scenario calculate the Upper Control Limit for an R chart that reflect 99.97% level of confidence. (2.5 points)

Question 25: Using the data contained in the scenario calculate the Lower Control Limit for an R chart that reflect 99.97% level of confidence. (2.5 points)

Question 26: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an R chart, which samples are out of control? (5 points)

Scenario: A canning company packages canned soup for a major soup manufacturer for distribution to regional wholesalers.  The company processes 5,000 cans of soup each day using an automated packaging machine that is programmed to fill each can with 74.0 ± 0.1 ounces net weight of soup.  The company's quality assurance process consists of randomly selecting five cans from the production line each hour and carefully weighing them. Sample observations for a 24-hour production run are reflected in the table below. 

Hour Sample 1 Sample 2 Sample 3 Sample 4 Sample 5
1 74.030 74.002 74.019 73.992 74.008
2 73.995 73.992 74.001 74.011 74.004
3 73.988 74.024 74.021 74.005 74.002
4 74.002 73.996 73.993 74.015 74.009
5 73.992 74.007 74.015 73.989 74.014
6 74.009 73.994 73.997 73.985 73.993
7 73.995 74.006 73.994 74.000 74.005
8 73.985 74.003 73.993 74.015 73.988
9 74.008 73.995 74.009 74.005 74.004
10 73.998 74.000 73.990 74.007 73.995
11 73.994 73.998 73.994 73.995 73.990
12 74.004 74.000 74.007 74.000 73.996
13 73.983 74.002 73.998 73.997 74.012
14 74.006 73.967 73.994 74.000 73.984
15 74.012 74.014 73.998 73.999 73.004
16 74.000 73.984 74.005 73.015 73.996
17 73.994 74.012 73.025 74.005 74.007
18 74.006 73.825 74.018 74.003 74.000
19 73.001 74.002 74.003 74.005 73.997
20 74.000 74.010 74.013 74.020 74.003
21 73.982 74.001 74.015 74.005 73.996
22 74.004 73.999 73.990 74.006 74.009
23 74.010 73.989 73.990 74.009 74.014
24 74.015 74.008 73.993 74.000 74.010
25 73.982 73.984 73.995 74.017 74.013

Question 27: Using the data contained in the scenario calculate the Upper Control Limit for an X-bar chart that reflect a 99.7% confidence level. (5 points)

Question 28: Using the data contained in the scenario calculate the Lower Control Limits for an X-bar chart that reflect a 99.7% confidence level. (5 points)

Question 29: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an X-bar chart, which samples are out of control? (5 points)

Question 30: Using the data contained in the scenario calculate the Upper Control Limit for an R chart that reflect 99.97% level of confidence. (5 points)

Question 31: Using the data contained in the scenario calculate the Lower Control Limit for an R chart that reflect 99.97% level of confidence. (5 points)

Question 32: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an R chart, which samples are out of control? (5 points)

Scenario: The manager of the customer service hotline for an internet service provider has been approached by the President of the company regarding a perceived increase in the number of customer complaints regarding the lack of timely technical assistance being provided by hotline technicians.  In order to evaluate the validity of the President’s concerns he decided to survey customers regarding their satisfaction with the timeliness of the technical assistance they received.  Surveys were conducted during a thirty-day period with one hundred fifty (150) randomly selected customers participating in the survey each day.  The number of customers surveyed who expressed dissatisfaction with the timeliness of the technical assistance they received is summarized in the following table.

Day No. Complaints  Day No. Complaints
1 22  16 15
2 29  17 17
3 25  18 17
4 17  19 19
5 20  20 22
6 16  21 23
7 34  22 27
8 11  23 29
9 31  24 33
10 29  25 21
11 15  26 24
12 10  27 22
13 33  28 24
14 23  29 23
15 27  30 31

Question 33: Using the data contained in the scenario calculate the Upper Control Limit for the number of complaints that reflect a 95.5% confidence level. (5 points)

Question 34: Using the data contained in the scenario calculate the Lower Control Limit for the number of complaints that reflect a 95.5%confidence level. (5 points)

Question 35: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for the number of complaints, which samples are out of control? (5 points)

Question 36: Using the data contained in the scenario calculate the Upper Control Limit for the proportion of complaints that reflect 95.5% level of confidence. (5 points)

Question 37: Using the data contained in the scenario calculate the Lower Control Limit for the proportion of complaints that reflect 95.5% level of confidence. (5 points)

Question 38: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for the proportion of complaints, which samples are out of control? (5 points)