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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 15minute 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 2021
Question 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 halfhour timeframe.
(5 points)
(b) Determine the likelihood that the dispensing machine will dispense more than 7 beverages in a 45minute timeframe.
(5 points)
(c) The dispensing machine supplied three beverages in a 10minute 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)

RUBRIC 

Excellent Quality 95100%

Introduction
4541 points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned. 
Literature Support 9184 points The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned. 
Methodology 5853 points Content is wellorganized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met. 

Average Score 5085% 
4038 points More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided. 
8376 points Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration. 
5249 points Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met. 

Poor Quality 045% 
371 points The background and/or significance are missing. No search history information is provided. 
751 points Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration. 
481 points There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met 

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MTH219 Probability and Statistics Fundamentals 
MTH219 Probability and Statistics Fundamentals