Statistics Exam

Midterm.xlsx

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Ch 15 Q 1 - 20 points

1. Consider the following time series data (temperature):
Month	Value	2 month MVA	Error	Squared Error	Exponential Smoothing 0.25	Error	Squared
1	64
2	68
3	75
4	81
5	87
6	93
7	96
8	98
9	92
10	83
11	72
a. Construct a time series plot. What type of pattern exists in the data?
b. Develop a two-month moving average for this time series. Compute MSE and a forecast for Month 12.
c. Use a α = 0.25 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for Month 12.
d. Compare the two-month moving average forecast with the exponential smoothing forecast using α = 0.25.
Which appears to provide the better forecast based on MSE?
e. Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller MSE than what you calculated for α = 0.25.
Alpha

Ch 15 Q 2 - 5 points

2. Using the same forecast values for problem 1, calculate a two-month weighted moving average with the following weights:
1/2 for the most recent observation 1/2 for the second most recent observation
Month	Value	2 month MVA	Error	Squared Error
1	64
2	68
3	75
4	81
5	87
6	93
7	96
8	98
9	92
10	83
11	72
a. What is the MSE for a 2 month weighted moving average?
b. By comparing the 2 month moving average from question 1 to the 2 month weighted moving average, which one is better and why?
c. By comparing the Exponential Smoothing at 0.25 from question 1 to the 2 month weighted moving average, which one is better and why?

Ch 9 Q 3 - 20 points

3. Draw a project network that can be used to assist in scheduling of the project activities:

Activity

Immediate Predecessor

E,H

B,G,D

F,K

I,J,K

L,M,N

Ch 9 Q 4 - 20 points

4. Consider the following project network and activity times (in weeks):
Activity	A	B	C	D	E	F	G	H	I	J
Immediate Predecessor	-	-	B	A,C	B	B	E	E	D,G	F,H
Expected	4	4	5	3	10	8	6	6	3	5
a. Identify the critical path
b. How much time will be needed to complete the project in weeks?
c. Can activity B be delayed without delaying the entire project? If so, by how many weeks?
d. Can activity H be delayed without delaying the entire project? If so, by how many weeks?
e. Can activity J be delayed without delaying the entire project? If so, by how many weeks?

Ch 10 - Q 5 - 20 points

5. Walmart SuperCenter (open 24 hours per day, every day) sells 16-packs of paper towels at a rate of about 840 packs per week (higher during the pandemic). Quality paper towels take a lot of space and the annual inventory cost is approximately $0.60 per pack. The cost to place an order for more is $45.00 and it takes 8 days for an order to arrive.

a. What is the optimal order Q* or EOQ quantity for Walmart?

b. What is the reorder point considering that Walmart is open 24/7?

c. How frequently should an order be replaced?

d. What is the reorder point for part (b) if the reorder point is expressed in terms of the inventory on hand rather than the inventory position?

e. Walmart warehouse has an area reserved to storage no more than 1,500 16-pack of paper towels. Should Walmart consider expanding the area reserved to storage 16-pack of paper towels?

Ch 11 Q 6 - 15 points

6. A private mechanic provides a single-server service. Customers provide an arrival rate of 2 cars per hour. The service rate is 3 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution.

a. What is the average number of cars in the system?

b. What is the average time that a car waits for the service to begin?

c. What is the average time a car spends in the system?

d. What is the probability that an arrival has to wait for service?

e. Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate and compute the probabilities that exactly 1, 2, and 3 cars will arrive during a 15-minute period.

EXTRA CREDIT - 15 points total

Extra Credit 1. You have been provided the following optimistic, most probable and pessimitic time in days for a bathroom remodeling:
Activity	Optimistic	Most Probable	Pessimistic
A	3	6	11
B	2	2	6
C	4	4	6
D	3	5	9
E	5	5	7
F	2	3	6
G	2	3	7
H	3	4	9
a. Calculate the Expected time:
b. Calculate the Variarnce:
Extra Credit 2. Once you have calculated the EOQ for problem 5, you will notice an amount that is not round.
You are trying to advise management whether perhaps you should round the value up or down by a considerable amount.
For example, if you find an EOQ of 1869, should you round it up to 1900 or should you round down to 1800. Minimum changes are not relevant.
Considering all factors, ordering costs, holding costs, and so on, what would you advise management?
Extra credit 3. For problem 6, let's say that we increase the service rate to 5 cars with the help of an assistant.
a. What is the average number of cars in the system now?
b. What is the new average time that a car waits for the service to begin?
c. What is the new average time a car spends in the system?
d. What is the new probability that an arrival has to wait for service?
e. By comparing arrival rate and service rate for problem 6 and adding an assistance who will cost the mechanic more money, will it be a smart move? Explain.