## Computing Cumulative Relative Frequency

0 | 6 | 3 | 4 | 5 |

3 | 6 | 4 | 2 | 1 |

2 | 3 | 1 | 6 | 2 |

3 | 6 | 4 | 2 | 5 |

4 | 2 | 6 | 2 | 2 |

4 | 4 | 1 | 6 | 2 |

4 | 4 | 3 | 1 | 1 |

4 | 6 | 3 | 4 | 2 |

3 | 5 | 5 | 4 | 1 |

5 | 5 | 5 | 2 | 1 |

1) What is the cumulative relative frequency when 4 widgets are sold?

A. 0.16

B. 0.22

C. 0.5

D. 0.72

Use the following data for the next question:

12.1 | 18.7 | 4.4 | 5.5 | 16.5 |

5.5 | 13.2 | 3.3 | 8.8 | 9.9 |

6.6 | 6.6 | 13.2 | 20.9 | 3.3 |

16.5 | 13.2 | 16.5 | 0 | 7.7 |

16.5 | 3.3 | 11 | 8.8 | 11 |

11 | 8.8 | 17.6 | 19.8 | 14.3 |

13.2 | 7.7 | 3.3 | 20.9 | 20.9 |

12.1 | 13.2 | 12.1 | 17.6 | 9.9 |

7.7 | 15.4 | 17.6 | 16.5 | 7.7 |

1.1 | 0 | 9.9 | 9.9 | 1.1 |

GM | Ford | Toyota | Total | |

car | 5 | 14 | 7 | 26 |

Truck | 6 | 1 | 3 | 10 |

Total | 11 | 15 | 10 | 36 |

## Random Probability Test

## Binomial Probability Distribution

##### Use the data below to develop a p-chart to answer questions 13 and 14

Day | Sample Size | Pizza's with Quality Issues |

1 | 25 | 2 |

2 | 25 | 1 |

3 | 25 | 3 |

4 | 25 | 2 |

5 | 25 | 1 |

##### Use the following data to construct a c-chart to answer questions 15 and 16.

Day | Complaints Received |

1 | 8 |

2 | 2 |

3 | 3 |

4 | 3 |

5 | 2 |

6 | 1 |

7 | 2 |

15) What is the upper control limit of the c-chart?

A. 10.856

B. 8.196

C. 2.714

D. 1.647

16) Which of the following are true about the process?

A. Special causes of variation are indicated

B. There are only common causes of variation

C. The process is not in control

D. Process is in control.

Use the following data to answer questions 17-19.

An assembly line pouring cereal into boxes pulls samples once an hour. In the chart below is the summary of ten boxes that are sampled each hour, including the mean weight of each sample and the range between the heaviest and lightest box of the sample. The table shows the results for a 6 hour period. All weights are recorded in ounces.

Hour | Mean weight | Range |

1 | 15.1 | 0.13 |

2 | 14.8 | 0.09 |

3 | 15.0 | 0.15 |

4 | 14.9 | 0.06 |

5 | 15.0 | 0.21 |

6 | 14.9 | 0.08 |

- 986 and 14.913
- 792 and 13.008
- 892 and 12.108
- 751 and 11.149

- 1405
- 2132
- 1746
- 3600

- The range is in control so the entire process is in control
- The mean is in control
- Special causes of variation are present for the process range.
- Special causes of variation are present for the process mean

##### Use this following information to answer questions 20-21:

Temp. | # boxes | |||||

67 | 12 | |||||

73 | 17 | |||||

88 | 28 | |||||

102 | 33 |

20) Compute the regression line to estimate number of ice cream boxes sold.

A. Y = 67 + 27.23X

B. Y = 33.52 + 21.2X

C. Y=-27.60+ 0.61X

D. Y = -43.52 + 4.5X

21) The correlation coefficient is

A. 0.58

B. 0.33

C. 0.76

D. 0.99

##### Use this information for Questions 22 – 26.

Sample data (as shown below) was collected on the weight of 5 vehicles (in lbs.) and associated fuel efficiency in Miles Per Gallon (MPG). The following is a partial Excel output that was reported.

22) What is the correlation coefficient for these variables?

A. 0.983

B. -0.984

C. 0.911

D. -0.911

E. 0.898

23) What is the regression equation?

A. Y = 7 + 1X

B. Y = 1 + 7X

C. Y = -1.38 + 99.3X

D. Y= 43.28 - 0.0063X

24) What can you say about the relationship between the weight of the vehicle and MPG?

A. 96.9% of variability in the MPG can be explained by the weight of the vehicle

B. 96.6% of variability in the weight of the vehicle can be explained by the MPG

C. 95.4% of variability in the MPG can be explained by the weight of the car

D. 95.4% of variability in the weight of the car can be explained by the MPG

25) What is the Standard Error?

A. 1.42

B. 2.32

C. 6.74

D. Cannot be computed

26) What is the SST?

A. 400.7

B. 170.7

C. 503.4

D. 521.2

##### Use the following data for problems 27 - 30

Month |
Sales |
|||||

Jan | 45 | |||||

Feb | 48 | |||||

Mar | 46 | |||||

Apr | 47 | |||||

May | 49 | |||||

June |

27) Using a two month moving average, what is the forecast for June?

A. 47.0

B. 30.5

C. 49.5

D. 48.0

28) Using a three month weighted moving average, compute a forecast for June with weights of 0.1, 0.4, and 0.5 (oldest data to newest data, respectively).

A. 32.3

B. 47.9

C. 48.9

D. 47.2

## Exponential Smoothing

29) Using exponential smoothing, with an alpha value of 0.3 and assuming the forecast for April is 44.0, what is the forecast for June?

A. 44.2

B. 48.2

C. 47.0

D. 46.9

30) What is the MAD value for the two month moving average?

A. 1.8

B. 1.0

C. 2.5

D. 3.0

31) You are examining four different forecasts and have calculated the following MAD levels:

• 2 Month moving average = 2.5

• 3 Month moving average = 1.5

• Exponential smoothing = 1.7 and

• Exponential Smoothing with Trend = 1.9

Which forecast is best?

A. 2 Month Moving Average

B. 3 Month Moving Average

C. Exponential Smoothing

D. Exponential Smoothing with Trend

Use the following data for problems 32 and 33

The table below shows sales (in thousands) for each quarter of the last three years

QTR1 | QTR2 | QTR3 | QTR4 | |

Year 1 | 11.5 | 7.2 | 5.1 | 14.2 |

Year 2 | 12.5 | 8.1 | 5.7 | 16.2 |

Year 3 | 13.8 | 9.0 | 6.2 | 17.8 |

32) What is the seasonal index for QTR4?

A. 0.25

B. 0.38

C. 0.17

D. 0.15

33) Using time series analysis, what is the forecast for QTR2 of the fifth year of sales?

A. 10.6

B. 55.6

C. 21.1

D. 8.1

Use the following information to answer Questions 34-37. Use space below for the network.

The table shown, below, reports a project’s activity times (in days) and precedence relationships.

activity | Time (days) | Predecessors |

A | 5 | NONE |

B | 6 | NONE |

C | 4 | A, B |

D | 15 | A, B |

E | 16 | A, B |

F | 8 | C, D |

G | 11 | C, D |

H | 9 | E |

I | 7 | F, G, H |

J | 4 | F, G, H |

34) What is your estimate of completion time for this project?

A. 26 days

B. 44 days

C. 39 days

D. 36 days

35) What is the critical path?

A. B, D, G, I

B. B, D, G, J

C. A, C, E, F, H, J

D. A, E, H

36) What is the Earliest Start (ES) time for activity G?

A. 10

B. 11

C. 21

D. 25

37) What is the slack for activity D?

A. 0 days

B. 1 day

C. 2 days

D. 3 days

Use the following information about a PERT project to answer question 38-39.

Times are in days. Assume only one critical path exists which is: A, E, F

Activity |
optimistic |
Most likely |
pessimistic |

A |
4 |
5 |
12 |

B |
9 |
12 |
15 |

C |
2 |
5 |
7 |

D |
15 |
17 |
25 |

E |
7 |
10 |
13 |

F |
3 |
5 |
8 |

38) What is the expected project completion time? Round off to the nearest integer.

A. 21 days

B. 19 days

C. 23 days

D. 53 days

39) What is the standard deviation of activity F?

A. 1.86 days

B. 0.83 days

C. 0.69 days

D. 3.47 days

Use the two POM crashing windows which appear on the next page to answer Question 40. Times are in days.

40) You are given a bonus of $1,750/day the project is complete early. What day will you complete the project to maximize your total bonus?

A. 59 Days

B. 56 Days

C. 53 Days

D. 50 Days

Use with Questions 39 and 40 | |||||||

Activity | Normal time | Crash time | Normal Cost | Crash Cost | Crash cost/pd | Crash by | Crashing cost |

Project | 59 | 46 | |||||

A | 15 | 12 | 15000 | 20000 | 1666.67 | 3 | 5000 |

B | 9 | 6 | 18000 | 26000 | 2666.67 | 0 | 0 |

C | 13 | 10 | 29000 | 40000 | 3666.67 | 3 | 11000 |

D | 10 | 8 | 10000 | 12000 | 1000 | 0 | 0 |

E | 8 | 5 | 20000 | 30000 | 3333.33 | 0 | 0 |

F | 9 | 6 | 12000 | 15000 | 1000 | 3 | 3000 |

G | 4 | 1 | 20000 | 24000 | 1333.33 | 0 | 0 |

H | 12 | 10 | 36000 | 40000 | 2000 | 2 | 4000 |

I | 10 | 7 | 5000 | 8000 | 1000 | 0 | 0 |

J | 6 | 5 | 4000 | 8000 | 4000 | 1 | 4000 |

K | 4 | 3 | 16000 | 20000 | 4000 | 1 | 4000 |

TOTALS | 185000 | 31000 |

Use with Questions 39 and 40 | |||||||||||||

Project time | Period cost | Cumulative cost | A | B | C | D | E | F | G | H | I | J | K |

59 | 0 | 0 | |||||||||||

58 | 1000 | 1000 | 1 | ||||||||||

57 | 1000 | 2000 | 2 | ||||||||||

56 | 1000 | 3000 | 3 | ||||||||||

55 | 1666.67 | 4666.67 | 1 | 3 | |||||||||

54 | 1666.67 | 6333.33 | 2 | 3 | |||||||||

53 | 1666.67 | 8000 | 3 | 3 | |||||||||

52 | 2000 | 10000 | 3 | 3 | 1 | ||||||||

51 | 2000 | 12000 | 3 | 3 | 2 | ||||||||

50 | 3666.67 | 15666.67 | 3 | 1 | 3 | 2 | |||||||

49 | 3666.67 | 19333.33 | 3 | 2 | 3 | 2 | |||||||

48 | 3666.67 | 23000 | 3 | 3 | 3 | 2 | |||||||

47 | 4000 | 27000 | 3 | 3 | 3 | 2 | 1 | ||||||

46 | 4000 | 31000 | 3 | 3 | 3 | 2 | 1 | 1 |