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QUESTION 1 Probability Show all calculations/reasoning Guide to marks: 16 marks - (a) 3, (b) 3, (c1) 3, (c 2-5) 1 each, (d) 3 (a) What is a random variable? What are the various types of random variable? Describe the difference between them. (b) What is meant by the term expected value? What does it measure? How is it computed for a discrete probability distribution? Give an example of its calculation. (c ) Consider the following record of daily sales of cars over the last 100 days. Sales Units (x) Number of days p(x) Exp Value More than Less than 1 20 2 40 3 20 4 10 5 10 Total 100 (1) Copy the above table and complete the missing column figures (note that the last 2 columns refer to cumulative probability distributions). Then answer the following questions highlighting the answers to (3), (4) and (5). (2) What was the probability of selling 1 or 2 units on any one day? (3) What were the average daily sales? (4) What was the probability of selling 3 or more? (5) What was the probability of selling 4 or less? (d) The average sales of apples is 5000 with a standard deviation of 500. (1) What is the probability that sales will be greater than 5500 apples? (2) What is the probability that sales will be less than 4900 apples? (3) What is the probability that sales will be less than 4250 apples? QUESTION 2 Research Question, Constructing data table and calculating probabilities Guide to marks: 14 marks – (1) 5, (2) 5, (3) 4 The following question involves learning/employing research skills in searching out data on the Internet, presenting it in a well constructed and informative table, and calculating some probabilities showing calculation methods. 1. Search the Internet for the latest figures you can find on the age and sex of the Australian population. 2. Then using Excel, prepare a table of population numbers (not percentages) by sex (in the columns) and age (in the rows). Break age into about 5 standard groups, eg, 0-14, 15-24, 25-54, 55-64, 65 and over. Insert total of each row and each column. Paste the table into Word as a picture. Give the table a title, and below the table quote the source of the figures. 3. Calculate from the table, showing your calculation methods: • The probability that any person selected at random from the population is a male. • The probability that any person selected at random from the population is aged between 15 and 24. • The joint probability that any person selected at random from the population is a female and aged between 15 and 34. • The conditional probability that any person selected at random from the population is 25 or over given that the person is a male. QUESTION 3 Statistical Decision Making and Quality Control Show all calculations/reasoning Guide to marks: 20 marks – (a) 3 each for 1,2, and 3, 1 for conclusion, (b) 10 A company wishes to set control limits for monitoring the direct labour time to produce an important product. Over the past the mean time has been 20 hours with a standard deviation of 10 hours and is believed to be normally distributed. The company proposes to collect random samples of 64 observations to monitor labour time. 1If management wishes to establish x control limits covering the 95% confidence interval, calculate the appropriate UCL and LCL. If management wishes to use smaller samples of 16 observations calculate the control limits covering the 95% confidence interval. Management is considering three alternative procedures in order to maintain tighter control over labour time: Sampling more frequently using 16 observations and setting confidence intervals of 90% Maintaining 95% confidence intervals and increasing sample size to 64 observations Setting 95% confidence intervals and using sample sizes of 36 observations. Calculate the control limits for each of the 3 alternatives. Which procedure will provide the narrowest control limits? What are they? (b) Hypothesis testing Company A has invested a great deal of time and money in occupational safety training for its employees and claims its occupational sick days are now below the national average. The national average was found to be 1.5 occupational sick days. per 100 employees with a standard deviation of 0.3 days. Company A randomly selected 100 employees for the last year and found the sample had a mean of 1.3 occupational sick days which Company A believed supported their claim. Using hypothesis testing with an alpha level of 0.05 and a 1-tail test, show the null and alternative hypotheses, sketch the distribution showing mean and critical region, and determine whether Company A’s belief is supported. END OF ASSIGNMENT 1 Rationale This assessment task covers topics 1 and 2: Probability concepts and distributions, and Statistical decision making and quality control. It has been designed to ensure that you are engaging with the subject content. More specifically, it seeks to assess your ability to: apply probability concepts to decision making demonstrate problems solving skills in assessing, organising, summarising and interpreting relevant information for decision making demonstrate understanding of the application of statistical hypothesis testing to decisions, with particular emphais on quality control. Marking criteria Assessment Item 1 The criteria described below will not apply to all parts of all questions but describe the standards expected where the question requirements are appropriate. It is expected that all students will complete their own work with no collusion with other students. Criteria High distinction Distinction Credit Pass Apply probability concepts to decision making Laws of probability well understood and applied without error to decision problems Laws of probability well understood and mostly applied without error to decision problems Laws of probability understood and applied appropriately to decision problems Laws of probability mostly understood and mostly applied appropriately to decision problems Assess, organise, summarise and interpret data Search the internet for appropriate data and summarise into tables and interpret meaningfully Search the internet for appropriate data and summarise into tables and interpret Search the internet for appropriate data and summarise into tables that can be interpreted meaningfully Search the internet and find appropriate data and summarise into tables that can be interpreted Apply statistical hypothesis testing to decisions with some emphasis on quality control Use of sample data to determine whether a statistical process is in control, with complete understanding of the relevant use of Z scores and t scores Use of sample data to determine whether a statistical process is in control, with mostly good understanding of the relevant use of Z scores and t scores Use of sample data to determine whether a statistical process is in control, with some understanding of the distinction between the use of Z scores and t scores Use of sample data to determine whether a statistical process is in control, with some understanding of the use of Z scores but less understanding of the use of t scores Presentation You should refer to the marking criteria for each assessment item. You should also follow the directions given in each question. Requirements: Present answers in the same sequence as the questions set. The front page of your assessment should consist of: subject code and subject name your name and student number assessment item number 3. Other pages should include: statement of academic integrity list of questions attempted student name and number on each page submitted pages should be numbered bibliography on last page The following link provides study resources such as referencing, writing, grammar, punctuation and study planning: http://student.csu.edu.au/study/resources Requirements This assignment must be submitted through Turnitin. It is recommended that your name, student ID and page number are included in the header or footer of every page of the assignment. Further details about submission in Turnitin are provided in online submission.



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