Order ID 53563633773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages Description/Paper Instructions
Assignment 2 – Part 2
Due October 16, 23:59 EST
Marks for each part of each question are indicated in parentheses. Please see the course outline for Part 2 Marking Scheme for penalties. There are no bonus marks for this assignment. Show your calculations for each question.
Total Marks: 20
Question 1 – Investment Outcomes (5 Marks)
Alan and his financial advisor Bob discuss risk measurement for investment options. Bob presents an investment with the possible outcomes and their associated probabilities given in the table below. He indicates that these probabilities are calculated based on past experience, industry rations and trends, and sophisticated simulation techniques.
Table 1 Probability Distribution of Outcomes for an Investment
Outcome Probability of Outcome Assumptions $300 20% Pessimistic $600 60% Moderately successful $900 20% Optimistic
- Use the probability distributing on the table to calculate the mean (expected value) and the standard deviation of the investment outcomes. What does the expected value imply here? (1 mark)
- Alan interprets the standard deviation of the investment outcomes as follows: “the larger the standard deviation (or spread of outcomes), the greater is the risk”. Explain why his interpretation of standard deviation makes sense. (1 mark)
- Alan compares two investments with the following means and standard deviations of the investment outcomes. Bob explains that investment A appears to have a high standard deviation, but not when related to expected value of the distribution. A standard deviation of $600 on an investment with an expected value of $6,000 may indicate less risk than a standard deviation of $190 dollars on an investment with an expected value of only $600. Calculate measure of coefficient of variation for investment A and B. Determine which investment carries the greater risk and explain why coefficient of variation is the appropriate measure to compare these investment opportunities? (1 mark)
Investment A
- = $6,000 σ = $600
Investment B
- = $600 σ = $190
- Alan compares three new investments with the following means and standard deviations of the investment outcomes. Calculate the coefficient of variation for investments 1, 2 and 3. Based on the coefficient of variation, which investment involves the most risk and the least risk? (1 mark)
Do we obtain the same results by comparing standard deviations of these investments? explain why? (1 mark)
Investment 1 Investment 2 Investment 3 µ = $600 µ = $600 µ = $600 σ=$20 σ = $190 σ = $300
Question 2 – Face Mask (5 marks)
Due to Covid-19 pandemic, the demand for disposable medical face mask has increased drastically. A particular brand of medical face mask making machine is used to produce disposable medical face masks in mass production. This machine is capable of producing 80 to 100 industry standard surgical style face masks every minute. This particular machine has a 2% defective rate. The production of medical face masks on this machine is considered a random process where each produced mask is independent of the others. Using this information calculate the following probabilities:
- What is the probability that the 10th medical face mask produced is the first with a defect? (1 mark)
- What is the probability that the face mask making machine produces no defective mask in a batch of 100? (1 mark)
- On average, how many face masks would you expect to be produced before the first defective mask? What is the standard deviation? (1 mark)
- Another brand of this machine that also produces surgical style face masks has a 5% defective rate where each mask is produced independently of the others. On average how many face masks would you expect to be produced with this machine before the first with a defect? What is the standard deviation? (1 mark)
- Based on your answers to parts (c) and (d), how does increasing the probability of an event (defect in this case) affect the mean and standard deviation of the wait time until the event’s occurrence (defect in this case)? (1 mark)
Question 3 – Blood Transfusion (5 marks)
A blood transfusion is a routine medical procedure in which donated blood is provided to you through a narrow tube placed within a vein in your arm. Blood types are important when it comes to transfusions. If you get a blood transfusion that that is not compatible with your blood type, your body’s immune system response will be triggered to fight the donated blood. For instance, a patient with Type O- blood can only receive Type O- blood, but a patient with Type O+ blood can receive either Type O+ or Type O-. Ethnic background is also important in blood transfusions. If a blood donor and recipient are of the same ethnic background, the chance of an adverse reaction may be reduced. According to a 10-year donor database of a particular country, 0.37 of white donors in the country are O+ and 0.08 are O-.
- Consider a random sample of 15 white donors in this country. What is the expected value of the number of individuals who could be a donor to a patient with blood type O+, and what is the standard deviation? (2 marks)
- Calculate the probability that 3 or more of individuals in the sample from part (a) could donate blood to a patient with O- blood type. (1 mark)
- On average, how many donors would need to be randomly sampled for the first type O+ donor to be identified? Assume that only while individuals are being tested. (1 mark)
- What is the probability that exactly 4 donors must be sampled to identify the first type O+ blood? Assume that only while individuals are being tested. (1 mark)
Question 4 – Poisson Distribution (5 marks)
Suppose that random variable x has a Poisson distribution with mean value = 2. (show your detailed answer for each part of questions below).
- Write down the Poisson formula and describe the possible values of x. (0.5 mark)
- Starting with the smallest possible value of x, calculate p(x) for each value of x until p(x) becomes smaller than 0.001. (1 mark)
- Create probability distribution graph for this Poisson distribution using your results from part (b). (0.5 mark)
- Calculate P(x = 2) (0.5 mark)
- Calculate P(x <= 4) (0.5 mark)
- Calculate P(1<= x <=4) (1 mark)
- Calculate P(2 < x < 5) (0.5 mark)
- Calculate P(2 <= x <6) (0.5 mark)
RUBRIC
QUALITY OF RESPONSE NO RESPONSE POOR / UNSATISFACTORY SATISFACTORY GOOD EXCELLENT Content (worth a maximum of 50% of the total points) Zero points: Student failed to submit the final paper. 20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. 30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. 40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. 50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. Use of Sources (worth a maximum of 20% of the total points). Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. 5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. 10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. 15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6th Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources. 20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment. Grammar (worth maximum of 20% of total points) Zero points: Student failed to submit the final paper. 5 points out of 20: The paper does not communicate ideas/points clearly due to inappropriate use of terminology and vague language; thoughts and sentences are disjointed or incomprehensible; organization lacking; and/or numerous grammatical, spelling/punctuation errors 10 points out 20: The paper is often unclear and difficult to follow due to some inappropriate terminology and/or vague language; ideas may be fragmented, wandering and/or repetitive; poor organization; and/or some grammatical, spelling, punctuation errors 15 points out of 20: The paper is mostly clear as a result of appropriate use of terminology and minimal vagueness; no tangents and no repetition; fairly good organization; almost perfect grammar, spelling, punctuation, and word usage. 20 points: The paper is clear, concise, and a pleasure to read as a result of appropriate and precise use of terminology; total coherence of thoughts and presentation and logical organization; and the essay is error free. Structure of the Paper (worth 10% of total points) Zero points: Student failed to submit the final paper. 3 points out of 10: Student needs to develop better formatting skills. The paper omits significant structural elements required for and APA 6th edition paper. Formatting of the paper has major flaws. The paper does not conform to APA 6th edition requirements whatsoever. 5 points out of 10: Appearance of final paper demonstrates the student’s limited ability to format the paper. There are significant errors in formatting and/or the total omission of major components of an APA 6th edition paper. They can include the omission of the cover page, abstract, and page numbers. Additionally the page has major formatting issues with spacing or paragraph formation. Font size might not conform to size requirements. The student also significantly writes too large or too short of and paper 7 points out of 10: Research paper presents an above-average use of formatting skills. The paper has slight errors within the paper. This can include small errors or omissions with the cover page, abstract, page number, and headers. There could be also slight formatting issues with the document spacing or the font Additionally the paper might slightly exceed or undershoot the specific number of required written pages for the assignment. 10 points: Student provides a high-caliber, formatted paper. This includes an APA 6th edition cover page, abstract, page number, headers and is double spaced in 12’ Times Roman Font. Additionally, the paper conforms to the specific number of required written pages and neither goes over or under the specified length of the paper. GET THIS PROJECT NOW BY CLICKING ON THIS LINK TO PLACE THE ORDER
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