The following task, in which you are asked to conduct a small number of simulation trials, should be done with manual calculations. Please be aware that the simulation results of such a small number of trials would not be sufficient for one to draw valid conclusions in a real situation. A large number of trials run on a computer would be necessary in order to arrive at a valid conclusion.

Given:

Management has asked you to help estimate the most likely cost per unit to produce a new product so that they can project profits at different selling prices. You are to simulate cost behavior using probabilistic simulation (Monte Carlo simulation) and have been provided with the following cost estimates. Materials cost will range between $33 and $39 per unit, labor between $22 and $28 per unit, and utilities between $3 and $6 per unit. The probability distributions of cost per unit are as follows.

Materials:

• The probability is .18 that the cost will be $33.

• The probability is .23 that the cost will be $35.

• The probability is .32 that the cost will be $38.

• The probability is .27 that the cost will be $39.

Labor:

• The probability is .12 that the cost will be $22.

• The probability is .18 that the cost will be $23.

• The probability is .22 that the cost will be $24.

• The probability is .28 that the cost will be $25.

• The probability is .20 that the cost will be $28.

Utilities:

• The probability is .26 that the cost will be $3.

• The probability is .43 that the cost will be $4.

• The probability is .31 that the cost will be $6.

Task:

A. Complete the attached “Simulation Template” to determine the following costs:

1. Average materials cost per unit

2. Average labor cost per unit

3. Average utilities cost per unit

4. Average total cost per unit

Note: Run 10 trials using the random numbers that are provided on the “Simulation Template” for each probability distribution. Use the random numbers in the exact sequence that they appear on the template for each cost.

Note: Submit your completed spreadsheet as an attachment to this task.

B. Determine the selling price per unit that should be established for this product using your simulation results and assuming that the company wants to realize an average markup of $20 on each unit sold.

• The probability is .43 that the cost will be $4.

• The probability is .31 that the cost will be $6.

Task:

A. Complete the attached “Simulation Template” to determine the following costs:

1. Average materials cost per unit

2. Average labor cost per unit

3. Average utilities cost per unit

4. Average total cost per unit

Note: Run 10 trials using the random numbers that are provided on the “Simulation Template” for each probability distribution. Use the random numbers in the exact sequence that they appear on the template for each cost.

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1) If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percentage of light bulbs have a life less than 2500 hours?

2) The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side?

3) The amount of Jen’s monthly phone bill is normally distributed with a mean of $60 and a standard deviation of $12. Fill in the blanks:

4) The amount of Jen’s monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25^{th} percentile.

5) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

6) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 88 inches, and a standard deviation of 10 inches. What is the likelihood that the mean annual precipitation during 25 randomly picked years will be less than 90.8 inches?

7) A final exam in Statistics has a mean of 73 with a standard deviation of 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?

8) A mean score on a standardized test is 50 with a standard deviation of 10. Answer the following

a. What scores fall between –1 and +1 standard deviation?

b. What percent of all scores fall between –1 and +1 standard deviation?

c. What score falls at +2 standard deviations?

d. What percentage of scores falls between +1 and +2 standard deviations?

1) For the following questions, would the following be considered “significant” if its probability is less than or equal to 0.05?

a. Is it “significant” to get a 12 when a pair of dice is rolled?

b. Assume that a study of 500 randomly selected school bus routes showed that 480 arrived on time. Is it “significant” for a school bus to arrive late?

2) If you flip a coin three times, the possible outcomes are HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. What is the probability of getting at least one head?

3) A sample space consists of 64 separate events that are equally likely. What is the probability of each?

4) A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, what is the probability that it is blue?

5) The data set represents the income levels of the members of a country club. Estimate the probability that a randomly selected member earns at least $98,000.

112,000 126,000 90,000 133,000 94,000

112,000 98,000 82,000 147,000 182,000

86,000 105,000 140,000 94,000 126,000

119,000 98,000 154,000 78,000 119,000

6) Suppose you have an extremely unfair coin: The probability of a head is ¼ and the probability of a tail is ¾. If you toss the coin 32 times, how many heads do you expect to see?

7) The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number of living out of an original 100,000 and the additional life expectancy for a person of that age. Determine the following using the table:

a. To what age may a female of age 60 expected to live on the average?

b. How many 60-year old females on average will be living at age 61?

c. How many 70-year old males on average will be living at age 71?

Describe an auto transformer starter. From the expression for power input per phase ( pro torque ) show that for turns ratio n of (root 3): 1 for the auto transformer:

the power input to the motor/phase = Vs^2*Rp/n^2*Zp^2

the motor starting torque = DOL torque/3

a. What is the estimated beta coefficient of your company? What does this beta mean in terms of your choice to include this company in your overall portfolio? b.Given the beta of your company, the present yield to maturity on U.S. government bonds maturing in one year (currently about 4.5% annually) and an assessment that the market risk premium (that is – the difference between the expected rate of return on the ‘market portfolio’ and the risk-free rate of interest) is 6.5%, use the CAPM equation in order to find out what is the present ‘cost of equity’ of your company? Explain what is the meaning of the ‘cost of equity’. c. Choose two other companies, look up their “Beta” and report the names of these companies and their betas. Suppose you invest one third of your money in each of the stocks of these companies. What will the beta of the portfolio be? Given the data in (b), what will the Expected Rate of Return on this portfolio be? Do you feel that the three-stock portfolio is sufficiently diversified or does it still have risk that can be diversified away? Explain

1. What was the main motivating factor for European maritime expansion in the sixteenth and early seventeenth centuries?

A. To increase economic opportunity

B. To seek out new lands for increasing populations

C. To spread Christian values

D. To conquer other empires or nations and take away local control

2. The root causes of the crisis that many states faced at the end of the second millennium B.C.E. were

A. natural disasters and external invasions.

B. external invasions and unstable governments.

C. migrations of foreigners and ecological fragility.

D. unstable governments and ecological fragility.

3. It’s believed that the role of feasts in the Ice Age was to

A. strengthen group ties.

B. celebrate weddings.

C. celebrate the resolution of serious conflicts.

D. mark times when food was abundant.

4. _______ was a kingdom on the Atlantic coast of Spain that traded with the Greeks and Phoenicians.

A. Fezzan

B. Tartessos

C. Etrona

D. Elche

5. A key technological development that began around 500 B.C.E. in sub-Saharan Africa was

A. yam cultivation.

B. monumental architecture.

C. writing.

D. iron smelting.

6. Which of the following archaeological evidence suggests that the Olmec were shamanistic?

A. Depictions of captives

B. Records of their mythology

C. Figurines of were-jaguars

D. Inscriptions describing religious observances

7. In forming his government, Asoka recruited what group to serve as bureaucrats?

A. Traditional Brahman elites

B. The military elite

C. The rising merchant class

D. The Buddhist clergy

8. The Chinese philosopher Xunzi wrote that if a person attempted to cure rheumatism by beating a drum and sacrificing a pig to the gods, then the

A. rheumatism would get better, but the person wouldn’t be happy.

B. rheumatism wouldn’t get better because proper therapy required playing a flute and sacrificing a chicken.

C. rheumatism would be cured.

D. drum would be worn out, and the pig would be gone.

9. Which of the following was a Chinese school of thought during the fourth century B.C.E. that denounced ethics in favor of obedience?

A. Legalism

B. Buddhism

C. Confucianism

D. Daoism

10. Which of the following is not one of the new thoughts of or about God that were formulated in the Axial Age?

A. Single God

B. Divine God

C. Many Gods

D. Involved God

11. How did Alfred the Great secure his modern reputation as a state-builder?

A. He forced people to live in militarized colonies.

B. He encouraged trade through tax incentives to merchants and businessmen.

C. He gave free land and tax breaks to peasants.

D. He was lavishly generous to monks.

12. In the Rome of Marcus Aurelius, a recurrent formula for saving the state from crisis involved

A. enlisting the aid of Persian allies.

B. dividing the government and delegating authority.

C. politicizing the military.

D. paying tributes to Germanic peoples in Europe.

13. In Mongol society, the expression “crane catching” referred to

A. successful leaders forcing submission from rivals.

B. a mysterious religious practice that’s little understood today.

C. the success of Mongol merchants in establishing long-term contracts with buyers.

D. the popular pastime of hunting birds.

14. What was the main reason for the isolation of Japan?

A. Domination by Chinese culture

B. Difficult navigation in surrounding seas

C. Weak rulers

D. Lack of education

15. Which of the following practices did the Ottomans use to strengthen their state?

A. The practice of religions other than Islam was forbidden.

B. Christian children were enslaved and brought up as Muslims to become Janissaries.

C. Missionaries were sent to remote areas to generate wealth.

D. Gifts were given to those who converted to Islam.

16. The economic security of the Inca Empire was based on

A. extensive trade with the Aztec Empire.

B. a horizontal compilation of terra firma.

C. intensive maize farming.

D. environmental diversity.

17. All of the following were a result of the Crusades except

A. increased hostility in Europe between Christians and Jews.

B. establishment of a large Christian kingdom in the Middle East.

C. a proclamation, by Zangi, calling for Jihad against the infidels.

D. destruction of peaceful relations between Muslims and Christians.

18. Which of the following is an example of new economic divisions in the European peasantry that began to occur during the fifteenth century?

A. Peasants living east of the Elbe River became freer.

B. Peasants throughout Europe became poorer.

C. Peasants living in the Balkans became freer.

D. Peasants living west of the Elbe River became freer.

19. During the sixteenth and seventeenth centuries, the major reason for the high death rate among Native Americans from disease was

A. warfare.

B. lack of immunities.

C. overwork.

D. malnutrition