Martha Washington Essays - George Washington, Daniel Parke Custis

Martha Washington Martha Washington lived a life full of love and sacrifice. She was born as a simple little girl Martha Dandridge to her plantation home in New Kent; she was married at 18 to become Martha Dandridge Custis. Still yet she was widowed at the age of twenty-six with two children and a land of over 17,000 acres to run on her own. Then she met a gentleman by the name of George Washington and Martha became the figure we know today as Martha Dandridge Custis Washington or Martha Washington. Martha was born on June 2, 1731 on the plantation near Williamsburg in New Kent, Chestnut Grove, to her father0, John Dandridge, and mother, Frances Jones Dandridge. She was the eldest daughter of the family and the spirited one. She enjoyed horseback riding, working in her gardens, sewing, dancing, she came to enjoy cooking, and it was said she had a great love for playing the spinet. Her father insisted that his children be educated, so he called for a tutor. The Dandridge children had lessons in the mornings before breakfast, Martha always dreaded them, especially spelling. She would much rather be out playing than sitting inside learning how some words were not spelled the same was as they sounded. Although these studies seemed like a waste of time then, later she would find that they would become quite useful. At the age of fifteen her mother was quite sure that she should learn to act like a lady and practice the etiquette of the day, she had began to help her mother with some of the chores around the house. It was also that same year that she was able to attend her first ball at Williamsburg. Young Martha Dandridge was extremely excited until she arrived at Williamsburg to find things quite different than what she expected and entered the ball to be terribly disappointed. She didnt know any of the other young ladies, who seemed to all know each other well, and she hadnt been prepared by the fashion of the day. She had made her dress herself and though it was of fine material it wasnt like that gowns imported from England that the other girls were wearing. She had not had her hair powdered like the rest of the girls, and she was completely miserable until she met Daniel Parke Custis. He seemed like an honest simple man in his thirties. He probably had an attraction to Marthas simple nature and beauty, Martha was about five feet tall with dark eyes and dark hair, so he asked her to dance. Suddenly simple Martha Dandridge had become the belle of the ball; she was dancing with one of the richest bachelors in Virginia. After a few years Martha and Daniel began to see more of each other and there was talk of an engagement, but first Daniel had to send off for his fathers permission to do so. Although Daniel was a man twenty years older than Martha was he was still under the rule of his father who had become bitter by his marriage and was angry with Daniel for refusing to marry the girl that his father had wished him to. Daniel came back to Martha with a grim look and had decided to give up; he thought it no use to argue with his father. His father was determined that he would not marry anyone that he didnt approve of, especially Martha for she wasnt even known; it was just impossible for his son to marry a nobody. Hurt, Martha went home to her mother in tears. She felt as if she wasnt good enough for the old man. She loved Daniel and wanted more than anything to be with him and the only thing that was stopping them was his father. The man who was miserable in his marriage and apparently wanted Daniel to be just as miserable as he was. Martha was scheduled to return back to New Kent that evening, but not if her mother and her cousin had anything to do with it. They had decided that Martha should stay two more weeks with her cousin Nat and his wife Dorthea, a very popular

The Israeli-Palestinian Conflict essays

The Israeli-Palestinian Conflict essays In the Middle East, disputes over territory are commonplace. One such dispute, the Israeli Palestinian conflict, is very controversial. In the 19th century, Israelis and Palestinians were able to coexist peacefully. The area now known as Israel was predominantly Muslim, but there were a significant amount of Jewish people. In the late 1800s a group in Europe decided to colonize this land. Known as Zionists, they were a minority of the Jewish population whose goal was to create a Jewish native land. They considered many locations, including areas in Africa and the Americas, before choosing Palestine. As Zionists settled in Palestine, many who intended to take over the land for a Jewish state, the indigenous Palestinian population became increasingly worried. Eventually, fighting broke out, with escalating waves of violence. Hitler's assent to power in Germany, along with Zionist happenings in western countries to disrupt efforts to place Jewish refugees in western countries, caused i ncreased Jewish immigration to Palestine. From there, conflict grew. There are two main problems in the middle of this conflict. First, there is the impact of the weak attempt to keep more ethnic states, especially since the area is very diverse. Second, the continued Israeli military occupation and confiscation of private land in the West Bank and control of Gaza, a highly repressive, with a minimum of Palestinians contributes to the conflict. Control over their lives and holds more than 10,000 Palestinian men, women and children in Israeli jails. Few of them have a legitimate trial and physical abuse and torture are common. The Palestinian border is controlled by the Israeli forces. This prevents women in labor from reaching hospitals, preventing food and medicine to Gaza, and the production of the growing humanitarian crisis larger. Israeli forces entered almost daily violated, kidnapping, and murder people. After the Oslo peace accords in 1993...

Classical Realism Essay Example | Topics and Well Written Essays - 1500 words

Classical Realism - Essay Example Elephant is a collection of short stories by Carver which includes the following: Boxes, Whoever Was Using This Bed, Intimacy, Menudo, Elephant, Blackbird Pie, and Errand. Carver used a "dirty realism" technique in presenting his thoughts in these short stories, "a North American literary construct born in the late 20th century where the narrative is stripped down to its fundamental features."2 A derivation of minimalism, dirty realism is present in most of the author's literary works, one essentially characterized by a focus on surface description and an economy of words. This literary genre is present in Elephant as it tends to eschew adverbs and allow context to dictate meaning.3 In minimalist stories, just like that of Carver's, the characters tend to be featured as unexceptional beings through the use of meaningful contexts and through incorporation of adverbs.4 Dirty realism is generally seen as a hallmark of Carver's Elephant as in the rest of his works. Setting out the differences between Carver's dirty realism and 19th century classical realism, the latter focuses on a broad category of artistic styles attempting to merge or combine classicism and realism in textual presentation. It is likewise broadly defined as "the faithful representation of reality", a literarily technique practiced by several schools of writing. Realism takes interest in scientific method, rational philosophy, and a reaction against the classic romanticism.5 It emphasizes "the immediate, the here and now, the specific action, and the verifiable consequence."6 The combination of classicism and realism seems to be an oxymoron, as classicism tends to idealize the subject matter while realism tends to develop a reaction against the idealists.7The 19th century realism tends to have a remarkable and monotonous agreement in main features. There is an excessive use of minute external detail, alongside with viewing the vaunted objectivity and impersonality as a faade for immorality and cynicism, neglecting the ideal. As rapid industrialization and urbanization take place, an expanding population and a rise in middle-class affluence provide an abundant ground for literary explorations, which is often regarded as "a strategy for imagining and managing the threats of social change."8 With Madame Bovary, the term was clearly established in France. Dickens was likewise held as "a novelist of the ideal or romantic school, welcoming the wholesome spirit of realism."9 As a dirty realist, Carver's objects are conveyed with a representational quality which may not be described as metaphorical, universal, or direct. His dirty realism is characteristically represented through truth and a depiction of commonplace events, characters, and settings. It considers characters and events which are very ordinary and uninteresting, attributing meaning and value to them.10 In his Elephant and Other Stories, he presents everyday objects in a realist, descriptive manner, with relevance to their relatedness in the syntax of sentences and the 'world' of the story.11 Intimacy, a story in the collection, suggests a constant fascination with animate objects with the character's expression of inexplicable things through the medium of objects depicted in the text. The story revolves around a man and his

Testing Required When Applying for a CE Mark for a Medical Device Essay

Testing Required When Applying for a CE Mark for a Medical Device - Essay Example The use of a PE tube is used to hold the cement after sterilization per prescribed, typical methods contained in the standards. The cement is mixed and inserted into the tube to a level flush with the tube. The cement used in a fresh state prior to implanting is also tested for microbiological contamination. As the testing requires a tube to contain the cement for testing a like size rod of equal diameter and length and sanitized per normal procedures will be used as the control. For long term testing of in bone, which is what is required in test the effects of the cement which will be used long term in actual application, selection of the species for test and control is contained in Figure 1 below: Implantation will be done through normally accepted surgical method including shaving the insertion area and thorough antiseptic cleaning of the area and surgery to implant should be performed to minimize any trauma to the area. After insertion sutures are used to close the site and ensure tubes do not loosen or move. After surgery observation is conducted of the test species at appropriate intervals to note and record per 3.3.4 of the standard â€Å"any abnormal findings, including local, systemic and behavioural abnormalities† (p. 5). At the completion of the testing period, in this case 78 weeks the animals will be euthanized humanely in order to determine the biological response of the test area to the prolonged contact with the cement â€Å"by grading and documenting the macroscopic and histopathological test responses as a function of time† (p. 5) and comparing it with the control material (the rods) and the surrounding area. The examination will be facilitated by use of a low magnification lens of each test site material. After all of these results have been documented, the test and control tubes and rods and the surround tissue/bone shall

Ethical Issues In Contractors Tendering Practices Construction Essay

Ethical Issues In Contractors Tendering Practices Construction Essay Ethics examine the morality of human conduct; it studies the basic principles of moral behaviour and is concern with the right or wrong of human behaviour. Every rational human being has an idea of what it is for something to be right or wrong, although sometimes it is difficult to evaluate what is wrong or right depending on the circumstance of such action (Etim, 1999). Business ethics is therefore a collection of moral principles or a set of values dealing with what is right or wrong, good or bad in business transactions. Such sets of values are being shared within the business community as well as the society as a whole. Moral ideas are considered to be inappropriate for everyday business dealings and some actions are disregarded due to the strong desire to make profit. Some have argued that ethics and business do not mix, and that the two are in direct conflict with each other. In fact, it has been said that companies that are truly ethical are going out of existence. Construction contracts can be obtained by negotiation or by competitive tendering (Shash, 1993; Ashworth, 2001). In competitive tendering, an owner invites a selected number of contractors to compete for the project. This method of tendering is considered as the most common means by which building and engineering contracting firms obtain works, and the dominant mechanism for allocating construction contracts (Ward, 1979; Yusif and Odeyinka, 2000; Ashworth, 2001; Hiyassat, 2001; Harris and McCaffer, 2001; Shen et al, 2004). The business of tendering for construction contracts has a large ethical component. Ethical principles in tendering are formally prescribed in the codes of conduct related to tendering process. The codes are designed to delegate responsibilities to both competing contractors and the client and to minimize the potentials for unethical practices. This work intends to examine cover pricing, collusive tendering and rate loading among other unethical practices which construction contractors sometimes engage in during tendering. Cover pricing in construction tendering Fu, Drew and Lo (2004) observe that contractors tendering behaviour is subject to their winning intent. It is however known that winning may not be the only objective in tendering. Although the tendering codes stipulates that tenderers shall only bid where they intend to carry out the work if successful, some contractors for some reasons sometime decide to submit tenders based on cover-price. Cover prices are tender prices which have been provided at rates specifically designed to lose the tender but which may appear to be competitive. Despite attempts to prevent this practice, several instances of cover pricing sometimes called non-serious tenders have been reported. When a contractor with a reasonable workload receives a set of tender documents from a reputable client and consulting organizations, the contractor has to decide what to do: first whether to do nothing, to return the tender documents or to submit a tender. A tender may be submitted in one of three ways: by obtaining a cover price, by preparing a tender based on accurate estimate, and by preparing a tender based on approximate estimate. The option to do nothing is not considered suitable due to the potential harm such a course of action might cause to the reputation of the contractor with the client, consultants and their business contacts. Also the option of returning the tender documents may be perceived by the contractor as unsatisfactory because it might mean exclusion from future tender list, although this should not be the case according to the code of procedure for tendering. Some reasons for the issuing of cover price by contractors to include: little interest in the contract; lack of resources to competently complete the work; shortage of time to compile tender; desire to remain considered for future contracts; and little chance of winning due to the large number competing contractors for the same contract. It is reported in Skitmore and Runeson (1999) that clients often give the perception that a failure to tender will prejudice a contracting firm in the future tendering exercise, and the consequence of this is the so called cover price which cannot easily be distinguished from a genuine competitive tender. Also, Runeson (1988) remarks that some tenders are based on cover prices not intended to win the contract and therefore above the expected price, and submitted to recover deposit moneys or to keep faith with the client or consultants. However, Lowe and Parvar (2004) provide a different perspective to cover pricing. They submit that tendering options available to a contractor are simply acceptance or rejection of the tendering opportunity, although, rejection does not mean that the contractor does not submit a tender. Unsatisfactory past experience with a particular client or consultants regarding personality or payment, high cost of tendering and inadequate information often resulted in inflation of the tender price (cover price) rather than a refusal to tender. Cover price can ruin the competitiveness of a tendering process and can also lead to collusion among tendering contractors. However, despite its unethical nature and illegality in some countries, there are some arguments in its favour. The shortage of time to compile a bona fide tender could compel a contractor to submit tenders based on cover price. The recognition of this fact may have prompted the Nigerian Institute of Quantity Surveyors (NIQS) in its Code of Procedure for Competitive Tender to state that: time allowed for completion of tender should relate to the scope of project. Adequate tendering time allows tenderers to obtain competitive quotations and thus, ensure the return of most competitive prices with least mistakes (Clause 4.2.1) Lowe and Parvar (2004) believe that only few contractors will actually decline an invitation to tender. However, it appears that contractors react differently to the perceived fear that the option of returning tender documents might exclude them from clientsà ¢Ã¢â€š ¬Ã¢â€ž ¢ future tender process The report of a survey of some Nigerian building contractors indicate that when they receive a set of tender documents at a time their firms have a reasonable workload, they return the tender documents to the clients or their representatives with an apology for their firmsà ¢Ã¢â€š ¬Ã¢â€ž ¢ inability to tender. Only a few contractors admit to engaging in the practice of cover pricing. Contractors who admit to using cover pricing in tendering reveal that their action is mostly driven by little or no interest in the contract under consideration and the desire to remain considered for future contracts and tendering process. Some contractors cited other reasons such as the personality of the cl ient, risk and unpredictability of the construction period as well as heavy workload as some reasons why cover pricing may be an option for their firms. Whether or not a cover price is provided with good intention, the fact remains that it results in lessening real competition of tenders. Collusion in Tendering Chen et al (2005) submit that one purpose of the standard tendering procedures is to reduce potential for collusion and manipulation of pricing. According to Ray et al (1999), collusion is a method of pricing control by contractors to substantially lessen competition. Collusive tendering occurs where several contractors have been invited to tender and the contractors agree among themselves either not to tender, or to tender in such a manner as not to be competitive with the other contractors. It has the effect of substantially lessening competition. The main reasons for this practice among contractors are that it provides: an even distribution of construction work for all the contractors involved a means of entering what is an apparently bona fide tender a means for discussion and agreement over illicit profit making such as amounts for cover price, and unsuccessful tendering fee. The practice, or possibilities for the practice of collusion is a factor among several other issues related to ethical tendering, and it is contrary to the ideals of competition. It only benefits those parties to the agreement at the expense of those outside, including clients and other contractors. Sheldon cited in Ray et al (1999), while examining collusion in the UK, holds that collusion agreement are seen as an attractive means of maintaining a steady flow of work and achieving higher, risk-adjusted, discounted profit. The tender codes of some countries clearly prohibit unethical practices such as collusion on tenders, inflation of prices to compensate unsuccessful tenderers or any such secret arrangements. The very fact that tendering contractors communicate with each other can be taken to be a form of collusive behaviour under competitive tendering process. Though, little evidence of collusive tendering seems to be available in Nigeria construction industry, it is pertinent for industry practitioners and clients to be aware of the possibility of such unethical practice. Rate loading Usually, a construction tender is priced in such a way that the prices of each item comprise the cost of that item plus a uniform percentage allowed as profit and overheads. This is not always the case. Contractors may mark up the bill items by different percentages to create some element of rate-loading in order to create a favourable cash flow. Two aspects of rate loading are front-end loading and claims loading. Construction contracts only become self-financing towards the completion of the project. Therefore contractors are required to engage a considerable amount of their own capital in the execution of the work, at least in the early stage. In an attempt to minimize the involvement of their capital and make the project self-financing at an early stage, they resort to price manipulations. Items which the contractor expects to be executed early in the project have prices which contain a disproportionately large content of overheads and profits and items to be executed in the later stage of the project have their prices reduced accordingly to maintain competitiveness (Fellows et al, 2002). This pricing strategy in construction tenders is referred to as front-end loading. Due to the time-value of money, the situation further benefit contractors but place a cash flow burden and greater risk on clients. There is also the practice of claims loading where contractors insert higher profit margin into unit rates related to those work items which they expect to be increased through variation orders during the execution of the contract (Xu and Tiong, 2002). Conclusion Unethical tendering practices such as cover pricing, collusive tendering and rate loading have the potential of reducing real competition and eroding the benefits of competitive tendering. They can also place enormous financial burden on client. Construction consultants therefore have a duty to carefully examine tenders for construction contracts to identify any such practice and possibly caution or sanction contractors who may have engage in these practices.

Hirschi Social Control Theory Essay

I agree with Hirchi’s Theory to a certain extent only. This is because I believe it is not applicable to all people and to all situations. Yes, it may be true that when a person, as early as his childhood, conforms to fit into groups and find his place, he will probably be a person who is responsible and law-abiding. While we still have our own self-interests and individuality, we all want to feel we belong and mould our beliefs and involvements to form attachments. Also, as stated by Hirchi’s Theory, conformity is formed by four variables which we develop through our interactions with family and school, the four being: attachment, commitment, involvement and belief. For me, attachment and conformity to different social groups in the society does not guarantee a person for him to be less ready in committing a crime. Yes, a human being’s personality is partly formed by the environment where he is in—may be the attachment and conformity with his environment helps in molding a righteous and morally-upright personality. But in humanism, a human being has the absolute control to his life. He has free will and it is up to him how he will react to the stimuli created by his environment. In addition, psychologically, the formation of personality is still debatable whether it is nature or nurture. Nature says that a human being’s personality is genetic and on the other hand, nurture says that personality is molded by his environment. I think that some criminals can still be counseled psychologically targeting areas where in he has not yet matured and where he is still fixated—some of these may be the lack of attachment to social groups.

Ch8 Test Bank

CHAPTER 8 SECTION 1: CONTINUOUS PROBABILITY DISTRIBUTIONS MULTIPLE CHOICE 1. Which of the following represents a difference between continuous and discrete random variables? a. Continuous random variables assume an uncountable number of values, and discrete random variables do not. b. The probability for any individual value of a continuous random variable is zero, but for discrete random variables it is not. c. Probability for continuous random variables means finding the area under a curve, while for discrete random variables it means summing individual probabilities. d. All of these choices are true. ANS:DPTS:1REF:SECTION 8. 1 2.Which of the following is always true for all probability density functions of continuous random variables? a. The probability at any single point is zero. b. They contain an uncountable number of possible values. c. The total area under the density function f(x) equals 1. d. All of these choices are true. ANS:DPTS:1REF:SECTION 8. 1 3. Suppose f(x) = 0. 25 . What range of possible values can X take on and still have the density function be legitimate? a. [0, 4] b. [4, 8] c. [? 2, +2] d. All of these choices are true. ANS:DPTS:1REF:SECTION 8. 1 4. The probability density function, f(x), for any continuous random variable X, represents: a. ll possible values that X will assume within some interval a ? x ? b. b. the probability that X takes on a specific value x. c. the height of the density function at x. d. None of these choices. ANS:CPTS:1REF:SECTION 8. 1 5. Which of the following is true about f(x) when X has a uniform distribution over the interval [a, b]? a. The values of f(x) are different for various values of the random variable X. b. f(x) equals one for each possible value of X. c. f(x) equals one divided by the length of the interval from a to b. d. None of these choices. ANS:CPTS:1REF:SECTION 8. 1 6.The probability density function f(x) for a uniform random variable X defined over the interval [2, 10] is a. 0. 125 b. 8 c. 6 d . None of these choices. ANS:APTS:1REF:SECTION 8. 1 7. If the random variable X has a uniform distribution between 40 and 50, then P(35 ? X ? 45) is: a. 1. 0 b. 0. 5 c. 0. 1 d. undefined. ANS:BPTS:1REF:SECTION 8. 1 8. The probability density function f(x) of a random variable X that has a uniform distribution between a and b is a. (b + a)/2 b. 1/b ? 1/a c. (a ? b)/2 d. None of these choices. ANS:DPTS:1REF:SECTION 8. 1 9. Which of the following does not represent a continuous uniform random variable? . f(x) = 1/2 for x between ? 1 and 1, inclusive. b. f(x) = 10 for x between 0 and 1/10, inclusive. c. f(x) = 1/3 for x = 4, 5, 6. d. None of these choices represents a continuous uniform random variable. ANS:CPTS:1REF:SECTION 8. 1 10. Suppose f(x) = 1/4 over the range a ? x ? b, and suppose P(X > 4) = 1/2. What are the values for a and b? a. 0 and 4 b. 2 and 6 c. Can be any range of x values whose length (b ? a) equals 4. d. Cannot answer with the information given. ANS:BPTS:1REF:SECTION 8. 1 11. What is the shape of the probability density function for a uniform random variable on the interval [a, b]? a.A rectangle whose X values go from a to b. b. A straight line whose height is 1/(b ? a) over the range [a, b]. c. A continuous probability density function with the same value of f(x) from a to b. d. All of these choices are true. ANS:DPTS:1REF:SECTION 8. 1 TRUE/FALSE 12. A continuous probability distribution represents a random variable having an infinite number of outcomes which may assume any number of values within an interval. ANS:TPTS:1REF:SECTION 8. 1 13. Continuous probability distributions describe probabilities associated with random variables that are able to assume any finite number of values along an interval.ANS:FPTS:1REF:SECTION 8. 1 14. A continuous random variable is one that can assume an uncountable number of values. ANS:TPTS:1REF:SECTION 8. 1 15. Since there is an infinite number of values a continuous random variable can assume, the probability of each individual value is virtually 0. ANS:TPTS:1REF:SECTION 8. 1 16. A continuous random variable X has a uniform distribution between 10 and 20 (inclusive), then the probability that X falls between 12 and 15 is 0. 30. ANS:TPTS:1REF:SECTION 8. 1 17. A continuous random variable X has a uniform distribution between 5 and 15 (inclusive), then the probability that X falls between 10 and 20 is 1. . ANS:FPTS:1REF:SECTION 8. 1 18. A continuous random variable X has a uniform distribution between 5 and 25 (inclusive), then P(X = 15) = 0. 05. ANS:FPTS:1REF:SECTION 8. 1 19. We distinguish between discrete and continuous random variables by noting whether the number of possible values is countable or uncountable. ANS:TPTS:1REF:SECTION 8. 1 20. In practice, we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but very large. ANS:TPTS:1REF:SECTION 8. 1 21. Let X represent weekly income expressed in dollars. Since there is no set upper limit, we cannot identify (and thus cannot count) all the possible values. Consequently, weekly income is regarded as a continuous random variable. ANS:TPTS:1REF:SECTION 8. 1 22. To be a legitimate probability density function, all possible values of f(x) must be non-negative. ANS:TPTS:1REF:SECTION 8. 1 23. To be a legitimate probability density function, all possible values of f(x) must lie between 0 and 1 (inclusive). ANS:FPTS:1REF:SECTION 8. 1 24. The sum of all values of f(x) over the range of [a, b] must equal one. ANS:FPTS:1REF:SECTION 8. 1 25.A probability density function shows the probability for each value of X. ANS:FPTS:1REF:SECTION 8. 1 26. If X is a continuous random variable on the interval [0, 10], then P(X > 5) = P(X ? 5). ANS:TPTS:1REF:SECTION 8. 1 27. If X is a continuous random variable on the interval [0, 10], then P(X = 5) = f(5) = 1/10. ANS:FPTS:1REF:SECTION 8. 1 28. If a point y lies outside the range of the possible values of a ran dom variable X, then f(y) must equal zero. ANS:TPTS:1REF:SECTION 8. 1 COMPLETION 29. A(n) ____________________ random variable is one that assumes an uncountable number of possible values.ANS:continuous PTS:1REF:SECTION 8. 1 30. For a continuous random variable, the probability for each individual value of X is ____________________. ANS: zero 0 PTS:1REF:SECTION 8. 1 31. Probability for continuous random variables is found by finding the ____________________ under a curve. ANS:area PTS:1REF:SECTION 8. 1 32. A(n) ____________________ random variable has a density function that looks like a rectangle and you can use areas of a rectangle to find probabilities for it. ANS:uniform PTS:1REF:SECTION 8. 1 33. Suppose X is a continuous random variable for X between a and b.Then its probability ____________________ function must non-negative for all values of X between a and b. ANS:density PTS:1REF:SECTION 8. 1 34. The total area under f(x) for a continuous random variable must equal _________ ___________. ANS: 1 one PTS:1REF:SECTION 8. 1 35. The probability density function of a uniform random variable on the interval [0, 5] must be ____________________ for 0 ? x ? 5. ANS: 1/5 0. 20 PTS:1REF:SECTION 8. 1 36. To find the probability for a uniform random variable you take the ____________________ times the ____________________ of its corresponding rectangle.ANS: base; height height; base length; width width; length PTS:1REF:SECTION 8. 1 37. You can use a continuous random variable to ____________________ a discrete random variable that takes on a countable, but very large, number of possible values. ANS:approximate PTS:1REF:SECTION 8. 1 SHORT ANSWER 38. A continuous random variable X has the following probability density function: f(x) = 1/4, 0 ? x ? 4 Find the following probabilities: a. P(X ? 1) b. P(X ? 2) c. P(1 ? X ? 2) d. P(X = 3) ANS: a. 0. 25 b. 0. 50 c. 0. 25 d. 0 PTS:1REF:SECTION 8. 1 Waiting TimeThe length of time patients must wait to see a doctor at an emergen cy room in a large hospital has a uniform distribution between 40 minutes and 3 hours. 39. {Waiting Time Narrative} What is the probability density function for this uniform distribution? ANS: f(x) = 1/140, 40 ? x ? 180 (minutes) PTS:1REF:SECTION 8. 1 40. {Waiting Time Narrative} What is the probability that a patient would have to wait between one and two hours? ANS: 0. 43 PTS:1REF:SECTION 8. 1 41. {Waiting Time Narrative} What is the probability that a patient would have to wait exactly one hour? ANS: 0PTS:1REF:SECTION 8. 1 42. {Waiting Time Narrative} What is the probability that a patient would have to wait no more than one hour? ANS: 0. 143 PTS:1REF:SECTION 8. 1 43. The time required to complete a particular assembly operation has a uniform distribution between 25 and 50 minutes. a. What is the probability density function for this uniform distribution? b. What is the probability that the assembly operation will require more than 40 minutes to complete? c. Suppose more time was allowed to complete the operation, and the values of X were extended to the range from 25 to 60 minutes.What would f(x) be in this case? ANS: a. f(x) = 1/25, 25 ? x ? 50 b. 0. 40 c. f(x) = 1/35, 25 ? x ? 60 PTS:1REF:SECTION 8. 1 44. Suppose f(x) equals 1/50 on the interval [0, 50]. a. What is the distribution of X? b. What does the graph of f(x) look like? c. Find P(X ? 25) d. Find P(X ? 25) e. Find P(X = 25) f. Find P(0 < X < 3) g. Find P(? 3 < X < 0) h. Find P(0 < X < 50) ANS: a. X has a uniform distribution on the interval [0, 50]. b. f(x) forms a rectangle of height 1/50 from x = 0 to x = 50. c. 0. 50 d. 0. 50 e. 0 f. 0. 06 g. 0. 06 h. 1. 00PTS:1REF:SECTION 8. 1 Chemistry Test The time it takes a student to finish a chemistry test has a uniform distribution between 50 and 70 minutes. 45. {Chemistry Test Narrative} What is the probability density function for this uniform distribution? ANS: f(x) = 1/20, 50 ? x ? 70 PTS:1REF:SECTION 8. 1 46. {Chemistry Test Narrative} Find the pr obability that a student will take more than 60 minutes to finish the test. ANS: 0. 50 PTS:1REF:SECTION 8. 1 47. {Chemistry Test Narrative} Find the probability that a student will take no less than 55 minutes to finish the test. ANS: 0. 75PTS:1REF:SECTION 8. 1 48. {Chemistry Test Narrative} Find the probability that a student will take exactly one hour to finish the test. ANS: 0 PTS:1REF:SECTION 8. 1 49. {Chemistry Test Narrative} What is the median amount of time it takes a student to finish the test? ANS: 60 minutes PTS:1REF:SECTION 8. 1 50. {Chemistry Test Narrative} What is the mean amount of time it takes a student to finish the test? ANS: 60 minutes PTS:1REF:SECTION 8. 1 Elevator Waiting Time In a shopping mall the waiting time for an elevator is found to be uniformly distributed between 1 and 5 minutes. 1. {Elevator Waiting Time Narrative} What is the probability density function for this uniform distribution? ANS: f(x) = 1/4, 1 ? x ? 5 PTS:1REF:SECTION 8. 1 52. {Elevator Wa iting Time Narrative} What is the probability of waiting no more than 3 minutes? ANS: 0. 50 PTS:1REF:SECTION 8. 1 53. {Elevator Waiting Time Narrative} What is the probability that the elevator arrives in the first minute and a half? ANS: 0. 125 PTS:1REF:SECTION 8. 1 54. {Elevator Waiting Time Narrative} What is the median waiting time for this elevator? ANS: 3 minutes PTS:1REF:SECTION 8. 1