MBA 6300 online Homework Assignment #1 complete solutions correct answers key

MBA 6300 online Homework Assignment #1 complete solutions correct answers key

MBA 6300 online Homework Assignment #1 - Statistics and Probability and Statistical Process Control

NOTE: Answers in boh words format and excel format

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

79.07

3

90.18

16

86.89

4

92.35

17

88.57

5

93.41

18

96.93

6

96.06

19

86.48

7

83.75

20

92.81

8

85.17

21

92.32

9

86.67

22

78.70

10

87.58

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

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, 10 students earned a B, 8 students earned a C, 7 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 85.25? (3 points)

Question 16. What is the probability that a randomly selected student’s score will fall between a standard Z-score of -1.61 and a standard Z-score of 1.28? (3 points)

Scenario Data: The mean time required to complete a certain type of construction project is 61 weeks with a standard deviation of 4.65 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

4, 6, 2, 9, 5

4

4, 5, 5, 4, 5

14

3, 2, 5, 4, 2

5

3, 7, 8, 5, 2

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

5, 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

73.051

16

74.000

73.984

74.005

72.455

73.996

17

73.994

74.012

72.965

74.005

74.007

18

74.006

72.841

74.018

74.003

74.000

19

73.698

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 twenty-five (125) 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)