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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?

Page 1 of 3

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

Page 2 of 3

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?

Page 3 of 3

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