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• Computing Cumulative Relative Frequency
• Random Probability Test
• Binomial Probability Distribution
• Exponential Smoothing

## Computing Cumulative Relative Frequency

Due to rounding, the answer you compute may not exactly match any of the options listed. Choose the option which comes closest to what you have computed.
Use the following data for number of widgets sold over a period of 50 days.

 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
2) What is the best class width according to the formulas in the text book:
A. 3
B. 4
C. 5
D. 6
3) What is the cumulative relative frequency of less than 12 minutes?
A. 0.20
B. 0.54
C. 0.74
D. 0.94
Z Values
4) In general, Z values will have which of the following attributes? (Best answer)
1 Positive for values above the mean.
2 Negative for values below the mean
3 Zero for values equal to the mean.
4 identifies the number of standard deviations of a particular value from the mean.
5 converts the value of x to a different set of units
6 z score has no units
A. Only 1, 2 5, 6 are true
B. Only 1, 2, 3 are true
C. All are true
D. Only 1, 2, 3, 4, 5
5) A data set of unknown distribution has a mean of 60 and a standard deviation of 7. At least how much of the data lies between 46 and 74? Hint: (Chebyshev)
A. 95%
B. 99.7%
C. 68%
D. 75%
Use this data for Questions 6-8:
 GM Ford Toyota Total car 5 14 7 26 Truck 6 1 3 10 Total 11 15 10 36

## Random Probability Test

6) What is the probability that a randomly selected vehicle is either a Ford or a car?
A. 0.75
B. 0.269
C. 0.067
D. 0.690
7) What is the probability that a randomly selected vehicle is a Toyota, given it is a car?
A. 0.75
B. 0.269
C. 0.067
D. 0.690
8) What is the probability that a randomly selected vehicle is a Toyota, given it is a car?
A. 0.75
B. B.0.269
C. 0.067
D. 0.69

## Binomial Probability Distribution

9) Consider a binomial probability distribution with p=0.35 and n=8. What is the probability of fewer than three successes?
A. 0.137
B. 0.258
C. .4278
D. .0318
10) Consider a binomial probability distribution with n=8, p=.35 calculate the probability of P(x>1)?
A. 0.0476
B. 0.8308
C. 0.3571
D. 0.4770
11) What is the expected mean of the amount of time spent on social media, assuming a uniform distribution of between 85 and 110 minutes?
A. 97.5
B. 99.8
C. 88.5
D. 100.1
12) An exponential probability has a  equal to 24 customers per hour. What is the probability a customer will arrive within the next 30 seconds?
A. 0.2389
B. 0.1813
C. 0.1940
D. 0.1834
##### Use the data below to develop a p-chart to answer questions 13 and 14
The data is from a local pizza parlor. Each day the management sampled 25 pizzas to see if they met the quality requirements of the business, making sure that the order had been fulfilled properly. The table below shows the number of pizzas that did not pass the quality check.
 Day Sample Size Pizza's with Quality Issues 1 25 2 2 25 1 3 25 3 4 25 2 5 25 1
13. What is the value of ?
A. 28
B. 7
C. 07
D. 4
14. What are the values of the UCL and the LCL
A. 194 and -0.082
B. 46 and 0 (LCL does not exist)
C. 056 and 0.006
D. 227 and 0 (LCL does not exist)
##### Use the following data to construct a c-chart to answer questions 15 and 16.
The data below represents the number of complaints recorded the customer service desk at a local call center. The data shows the number of complaints logged each day over a seven day period.
 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
17.What is the UCL and LCL of the control chart?

1. 986 and 14.913
2. 792 and 13.008
3. 892 and 12.108
4. 751 and 11.149
18. What is the UCL of the range control chart?
1. 1405
2. 2132
3. 1746
4. 3600
19. What did we learn about the process from the control charts?
1. The range is in control so the entire process is in control
2. The mean is in control
3. Special causes of variation are present for the process range.
4. Special causes of variation are present for the process mean
##### Use this following information to answer questions 20-21:
The following sample data taken from the “Back of the Bike” ice cream company, and. contains the temperature (Temp.) and the number of boxes of ice cream sold (#boxes):
 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