MTH219 Fundamentals of Statistics and Probability

This  assignment  is worth  16%  of  the  final  mark  for  MTH219  Fundamentals  of  Statistics  and    Probability.The cut-off date for this assignment is 26 August 2020 (Wednesday), 2355 hours. Note to Students:You      are      to      include      the      following      particulars      in      your      submission: CourseCode_AssignmentCode_UserID_FullName.  For example, ABC123_TMA01_Sally001_TanMeiMeiSally (omit D/O, S/O). Use underscore and not space.In the endemic phase of a virus spread, testers are employed to carry out a random testing in a community of 400,000 people. There are a total of 8 testers, each tasked to test 20 persons per day randomly selected from the community, over a duration of 90 days. There is no repeated testing  of  any  individual.  The  number  of  persons  who  tested  positive  on  a  daily  basis  is  submitted by each tester and provided in the file “test_results.csc’.You are engaged as a member of a data analytics team in investigating the testing results and to submit a typed-report addressing the following questions. You are to use the functionalities of a spreadsheet wherever possible. (a)Consolidate  the  data  from  all  8  testers.  Then,  plot  the  distribution  of  the  number  of  positive cases per day (per tester) over the entire dataset. (The total number of samples in your entire distribution will be 8✕90 = 720 in this case.) (10 marks)(b)Your team leader suspects that the number of positive cases per day follows a binomial distribution. By considering the conditions for such a model, demonstrate why it might be suitable.(10 marks)(c)By  comparing  the  PMF  of  a  binomial  model  with  the  chart  obtained  in  part  (a),  determine the probability of contracting the virus for any individual by trial and error, up  to  ONLY  1  decimal  place.  Then,  plot  the  distribution  of  the  predicted  number  of  positive  cases  per  day  using  the  binomial  model  in  the  same  graph  with  the  actual  distribution (shown in part (a)) and discuss the accuracy of the model.(20 marks)(d)The team leader has been informed that one of the 8 testers received a faulty batch of test kits that was used throughout the 90 days. Describe and execute your strategy to discover this tester. What is wrong with the test-kits used by this tester? Remove the faulty  test  results  and  graph  the  comparison  between  the  predicted  and  actual  cases  again. State your observation. (20 marks)
MTH219Tutor-Marked AssignmentPage 3 of 3 (e)A team member suggests that there is a more than 10% chance that at least 8 persons out of 20 tested will be positive cases. Using your binomial model, explain the reasons to support or reject this claim.(10 marks)(f)For only tester 7, calculate the mean, standard deviation, median, third quartile and 90th percentile of his testing results.(10 marks)(g)Plot the PMF and CDF of the geometric distribution from the Bernoulli trial of the virus test for each tester per day. Hence, compute the probability that a tester obtains the first positive case within the 20 tests allocated in a single day. Why is this probability not 1?(10 marks) The  remaining  10  marks  will  be  awarded  based  on  the  quality  of  report  writing  and  presentation,  based  on  criteria  such  as  formatting,  clarity  and  logic  of  explanations,  use  of  charts/figures and spelling/grammatical errors etc