Management has asked you to help estimate the most likely cost per unit to produce a new product

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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.

If light bulbs have lives that are normally distributed with a mean of 2500 hours

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Data File 3
Show all work


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 25th 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?
Chapter Six

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?

A+ Answer



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

APPLE COMPANY

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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

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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

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1. For most people, the religious revival of the eighteenth century focused on



A. individual study of the scriptures.

B. feelings and enthusiasm.

C. returning to organized religions that had successfully dealt with public corruption.

D. a scientific and reasoned approach to faith.



2. The Treaty of Westphalia of 1648



A. ended the wars of religion through a policy of tolerance.

B. came close to establishing the power of the Roman Church in England.

C. gave rulers the right to impose their religion upon their subjects.

D. ended civil wars throughout Europe.



3. During the sixteenth and seventeenth centuries, Japan was the world's leading producer of



A. silver.

B. porcelain.

C. pepper.

D. rhubarb.



4. Probably the most lasting contribution of Napoleon's rule was



A. his understanding of the role of the military.

B. his legal code.

C. abolishing the aristocracy and subordinating the church to the state.

D. redrawing the map of Europe.



5. For the English philosopher Jeremy Bentham, social institutions should be evaluated on the basis of their



A. ability to provide services at the lowest cost.

B. imposing minimal intrusions into citizens' lives.

C. success in providing the greatest good to the greatest number.

D. concern for the rights of the individual over social utility.



6. Quinine was essential for the expansion of imperial powers because of its



A. value as a base for cosmetics.

B. usefulness in fighting malaria.

C. value for flavoring and preserving food.

D. role as a military weapon.



7. Who wrote, "Here is the slave, there is the master; there is the wealth of some, here is the poverty of most . . . Here humanity attains its most complete development and its most brutish"?



A. Samuel Smiles

B. William Blake

C. Karl Marx

D. Alexis de Tocqueville



8. Comte de Gobineau, a French anthropologist, argued that human beings



A. could be classified by race, with the French at the top and Asians at the bottom.

B. could be classified by race, with the whites at the top and blacks at the bottom.

C. were all the same, regardless of race.

D. could be classified by race, but non-Europeans who adopted European culture could evolve to a higher state of being.



9. Constitutionalism is best defined as



A. a set of beliefs that guarantees equal rights to all the citizens of a state.

B. a doctrine that the state is founded on rules established by citizens and rulers to which all are bound.

C. the creation of a specific document or constitution.

D. a document that outlines democratic principles.



10. China began to industrialize in the 1860s due to



A. economic decline in the face of European expansionism in Asia.

B. defeat by Britain and the decline of its tea market.

C. a peasant rebellion and foreign military occupation.

D. its failure to defeat Japan and Britain.



11. Who ruled over Babylon's last era of greatness?



A. Senacherib

B. Ashurbanipal

C. Nebuchadnezzar II

D. Nabopolassar

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Logically, check the longest time. Since 12 divides 84, when Uranus is done its orbit, Jupiter is always going to lined up. The one to check is Saturn. What multiple of 84 is divisible by 30? Check them in order.
84?
168?
252?
336?
420? 

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In designing algorithms, we have to accomplish a certain objective. Three algorithms are given below. 

What does each algorithm accomplish when the initial values of x and y are 2 and 3, respectively? 

What are the final values for x and y for each algorithm? 

Assuming that setting up variables is more efficient than performing mathematical operations, which one is more efficient and why?



1: t1 = x; t2 = y; x = t2; y = t1

2: z = x; x = y; y = z

3: x = x + y; y = x – y; x = x – y

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1. A coin-operated drink machine was designed to discharge a mean of ounces of coffee per cup. In a test of the machine, the discharge amounts in randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were ounces and ounces, respectively. If we assume that the discharge amounts are normally distributed, is there enough evidence, at the level of significance, to conclude that the true mean discharge, , differs from ounces?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
2
It was claimed recently that more than of high school students in the United States use computers for educational purposes. We wish to examine this claim. We choose a random sample of U.S. high school students and find that of these students use computers for educational purposes. Based on this, can we conclude, at the level of significance, that more than of high school students in the United States use computers for educational purposes? In your answers, denote the proportion of all U.S. high school students who happen to use computers for educational purposes by. Perform a one-tailed test. Then fill in the table below.Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Can we conclude that more than 60% of high school student in the u.s use computers for educational purposes? Yes or NO
3
An industrial plant wants to determine which of two types of fuel, electric or gas, is more cost efficient (measured in cost per unit of energy). Independent random samples were taken of plants using electricity and plants using gas. These samples consisted of plants using electricity, which had a mean cost per unit of and standard deviation of, and plants using gas, which had a mean of and standard deviation of. Assume that the populations of costs per unit are normally distributed for each type of fuel, and assume that the variances of these populations are equal. Can we conclude, at the level of significance, that the mean cost per unit for plants using electricity, , differs from the mean cost per unit for plants using gas,?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table
4
At LLD Records, some of the market research of college students is done during promotions on college campuses, while other market research of college students is done through anonymous mail, phone, internet, and record store questionnaires. In all cases, the company solicits an "intent-to-purchase" score from the student, with being the lowest score ("no intent to purchase") and being the highest score ("full intent to purchase").
The manager finds the following information for intent-to-purchase scores for a soon-to-be-released CD:

Suppose that the five populations of scores from which these samples were drawn are approximately normally distributed and have the same mean and the same variance.
Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place.
6
A manufacturer claims that the mean lifetime, , of its light bulbs is months. The standard deviation of these lifetimes is months. Ninety bulbs are selected at random, and their mean lifetime is found to be months. Can we conclude, at the level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from months?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)
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