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(Solved) Hello Looking for the solution for these questions Thanks


Hello

Looking for the solution for these questions

Thanks


Week 1 Homework Assignment

 

1. Historical data indicates that the time required to complete a particular type of project

 

follows a normal distribution with a mean completion time of 45 weeks and standard

 

deviation of 3 weeks.

 

a. What is the probability of completing the project in no more than 41 weeks?

 

b. What is the probability of completing the project in no less than 48 weeks?

 

2. Students enrolled in a particular course are preparing for an exam that will consist of 25

 

multiple choice questions, each of which has five possible answers.

 

a. What is the probability of a student correctly answering no less than 22 questions

 

based solely upon guessing the answer to each question?

 

b. What is the probability of a student correctly answering no more than 18

 

questions based solely upon guessing the answer to each question?

 

c. What is the probability of a student correctly answering exactly 13 questions

 

based solely upon guessing the answer to each question?

 

3. 50 students enrolled in a particular course recently completed a mid-term exam. 13

 

students earned an A, 10 students earned a B, 8 students earned a C, 9 students earned a

 

D, and 10 students earned an F on the exam. The students were queried regarding the

 

number of hours they had devoted to studying for the exam. 11 of the students who

 

earned an A, 7 of the students who earned a B, 3 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.

 

a. What is the probability of a randomly selected student having devoted no more

 

than 8 hours to studying for the exam?

 

b. What is the probability of a randomly selected student having earned an A or a B

 

on the exam, given they devoted no more than 8 hours to studying for the exam?

 

c. What is the probability of a randomly selected student having earned less than a B

 

on the exam given, they devoted more than 8 hours to studying for the exam?

 

d. What is the probability of a randomly selected student having earned less an A on

 

the exam, given they devoted more than 8 hours to studying for the exam?

 


 

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4. A company that operates a production line that fills 16 ounce boxes of pasta shells uses a

 

quality assurance process that involves randomly selecting and weighing four boxes

 

every hour. The sample data collected during a particular eight-hour shift is as follows:

 

Box No.

 

Hour No.

 

1

 

2

 

3

 

4

 

5

 

6

 

7

 

8

 


 

1

 

15.97

 

16.13

 

15.98

 

15.85

 

15.99

 

15.97

 

16.01

 

16.00

 


 

2

 

16.00

 

16.12

 

15.92

 

16.00

 

15.98

 

16.10

 

15.92

 

15.97

 


 

3

 

16.01

 

16.15

 

15.95

 

15.98

 

16.07

 

16.04

 

16.03

 

16.03

 


 

4

 

16.02

 

16.12

 

15.96

 

16.15

 

16.00

 

16.02

 

16.05

 

15.98

 


 

a. What are the values for the lower and upper controls limit for x-bar using a 99.7%

 

level of confidence?

 

b. Prepare a x-bar chart that reflects upper and lower control limits for x-bar, xdouble bar, and x-bar for each hour. Based upon the x-bar chart, for what specific

 

hours was x-bar outside the control limits during the eight-hour period?

 

c. What are the values for the lower and upper controls limit for R using a 99.7%

 

level of confidence?

 

d. Prepare a R chart that reflects the upper and lower control limits for R, R-bar, and

 

R for each hour. Based upon the R chart, for what specific hours was R outside

 

the control limits during the eight-hour period?

 

5. The manager of a local bank perceives that there has been an increase in the incidence of

 

customer?s complaints regarding excessive waiting times at the drive-thru teller window.

 

The manager surveyed twenty randomly selected drive-thru teller window customers

 

daily for a period of fourteen days. The number of customers who indicated they had

 

experienced excessive waiting times was as follows. Each instance of a customer

 

indicating they had experienced an excessive waiting time constitutes a defect.

 

Day No.

 

1

 

2

 

3

 

4

 

5

 

6

 

7

 

8

 

9

 

10

 

11

 


 

No. Complaints

 

2

 

3

 

7

 

2

 

2

 

8

 

8

 

7

 

8

 

2

 

2

 

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Day No.

 

12

 

13

 

14

 


 

No. Complaints

 

6

 

2

 

2

 


 

a. What are the values for the lower and upper controls limit for the percent defects

 

using a 95.5% level of confidence?

 

b. Prepare a p-chart that reflects the upper and lower control limits for p, p-bar, and

 

p for each day. Based upon the p-chart, for what specific days was the percent

 

defective outside the control limits during the fourteen-day period?

 


 

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DATE ANSWERED

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