MTH219 Probability and Statistics Fundamentals
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
MTH219 Probability and Statistics Fundamentals
STUDENTS’ INSTRUCTIONS:
1. There are SIX (6) questions and SIX (6) pages in this Timed Online Assignment (TOA) (including cover page).
2. You must respond to all of the questions.
3. Before attempting a question, if you have any questions or believe there is an error in the question, quickly explain your understanding and assumptions about it.
4. At the end of this TOA, you MUST submit your answers via Canvas (similar to TMA submission) (as stated on this cover page). The 15-minute grace period displayed on Canvas is only for technical issues that arise during the submission process. You will not be allowed to submit your answers after then, and you will be considered to have dropped out of the course. There will be no opportunity to appeal.
5. In your submission, you must include the following information: SUSS PI Number, TOA Course Code, and Full Name TOACourseCode FullName StudentPI should be the name of your submission file. Use an underscore instead of a space. TOAXYZ RaphaelLee T1923161 (omit D/O, S/O) is an example.
6. Your submission should only contain one file that is no more than 500MB in size.
It must be a PDF or a Microsoft Word document in the.doc or.docx format. All responses must be typed. Flowcharts and graphs can be scanned or photographed and then included in a PDF or Word file as long as the file size does not exceed 500MB.7. Ensure that the question number is clearly given on each page for replies that cannot be typed and must be handwritten. All handwritten answers that are uploaded must be legible, readable, and full. Unreadable or incomplete photos will not receive any points.
Turnitin will examine your material to avoid plagiarism and collusion.
Only the marker will have access to the Turnitin report; you will not be able to see it.
9. Plagiarism and collusion are significant offenses at the University, and your Turnitin report will be thoroughly scrutinized as part of the grading process.
10. Unless otherwise indicated, complete details of each question’s operation must be supplied.Complete all of the questions. (A total of 100 points)
the first question
Thirty students who had been taught in such tests and twenty students who had not took a test with marks ranging from 0 to 100 were given the same test. The results are summarized in Table Q1 below.
Standard deviation of the mean
30 trained pupils, 62 unskilled students, and 20 untrained students 12 52
Q1 Table
(a) Calculate the combined set of 50 scores’ mean and standard deviation. Give two decimal places to your responses.
[Hint: you can use the following formula: variance, 2 = ( ) 2=s1
] [ 2 ] [ 2 ] [ 2 ] [ 2 ] [ 2 ] [ 2 ] [
(10 points)
(a) Despite being unwell, one of the students took the test and received only one point. It was decidedsto exclude this result from the analysis.
I Find the average and standard deviation of the remaining 49 scores.
Give two decimal places to your responses.
(6 points)
(ii) Describe the differences in the mode and median when compared to the whole set of 50 scores.
(4 points)
MTH219 Page 4 of 6 Copyright 2021 Singapore University of Social Sciences (SUSS)
TOA for the January Semester of 2021Question 2: The proportion of defective goods in a batch of manufactured items is p. A random sample of nine is collected from each batch and tested. The batch is rejected if two or more items are determined to be defective; otherwise, it is approved.
(a) Demonstrate that the likelihood of a batch being accepted is (1 + 8).
(6 points)
(a) It is determined to change the inspection scheme so that if one defect is discovered in a sample, a second sample of nine is taken and the batch is rejected if any defects are detected in this sample. The original scheme is maintained with this exception.
I Using the updated scheme, calculate the likelihood of a batch being accepted in terms of p, simplifying your answer as much as feasible.
(6 points)
(ii) Using this new sampling technique, evaluate and comment on the average number of items sampled over a large number of batches when p = 0.1.
Give your answer to the nearest two decimal places.
(8 points)
Question 3: A drink dispenser dispenses either tea or coffee cups. The number of cups of tea sold is a Poisson variable with a mean of 0.5 cups every 10 minute interval, while the number of cups of coffee sold is a Poisson variable with a mean of 1.5 cups per 10 minute period.
(a) Determine the chance that the dispensing machine will dispense exactly 2 cups of tea and 2 cups of coffee in a half-hour timeframe.
(5 points)
(b) Determine the likelihood that the dispensing machine will dispense more than 7 beverages in a 45-minute timeframe.
(5 points)
(c) The dispensing machine supplied three beverages in a 10-minute period.
Calculate the likelihood that these were all coffee cups.
(5 points)Question 4: The number of buses “74” arriving at the bus stop outside the SUSS campus is a Poisson variable with a rate of 9 buses per hour during peak hours.
(a) Determine the likelihood of having to wait more than 20 minutes for the bus “74” if one bus “74” had just left when you arrived at the bus stop. Show all of your work in depth.
(6 points)
(a) Explain briefly if you should expect to wait longer at the bus stop if the bus “74” has just left when you arrive.
(4 points)
Question 5: The average married man’s height in a city is 180 cm, with a standard deviation of 4 cm, while the average married woman’s height is 175 cm, with a standard variance of 3 cm. Assume that height has no bearing on your marriage partner selection. At random, a couple is chosen. For the next computations, show all of your workings in detail.
(a) Determine the likelihood that I they are both taller than 177.5cm; (4 marks); (ii) the spouse is taller by less than 5cm; (4 marks); and (iii) their height difference is less than 5cm.
(4 points)
(a) Seven more married couples from the city are chosen. Calculate the likelihood that at least two of the chosen couples have a height difference of more than 5cm.
(8 points)Question 6: An insect’s life in days, X, is regularly distributed with a mean of 2 days and a standard deviation of 0.2 days.
(a) Determine the likelihood that an insect will live for I more than 200 days; (3 marks) or (ii) between 50 and 150 days.
(4 points)
T1 and T2 are the life expectancies of two insects, and = 1 2.
I If their life expectancies are independent, show and characterize the log10 distribution type.
(4 points)
(ii) Is it important that one bug has 1.8 times the life expectancy of the other?
(4 points)
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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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