Assessment item 1
Assignment 1
Value: 10%
Due date: 16-Aug-2016
Return date: 07-Sep-2016
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Alternative submission method
Task
QUESTION 1 Probability
Show all calculations/reasoning
20 marks - 4 for 1(a), 4 for 1(b), 4 for 1(c), 5 for 1(d), 3 for 1(e)
(a) Describe the two basic laws of probability.
(b) What is the expected value and what does it measure? How is it computed for a discrete probability distribution?
(c) Consider the following record of sales of iPhone SEs for the last 25 days.
SALES UNITS NUMBER OF DAYS
8 5
9 3
10 12
11 3
12 2
TOTAL 25
1. What was the probability of selling 9 or 10 units on any one day?
2. What were the average daily sales?
3. What was the probability of selling 9 or more?
4. What was the probability of selling 11 or less?
(d) There is a cage of 80 unwanted kittens. 36 are female (F) and black (B); 14 are male (M) and black (B); 17 are female and tabby coloured (T); 13 are male and tabby coloured (T).
1. Using Excel construct a table showing gender in the rows and colour in the columns with total of rows and columns. Then paste this Excel table into Word.
2. Now calculate the probability of a kitten being:
(i) Female
(ii) Tabby coloured
(iii) Black given a male
(iv) Tabby coloured given a female
(e) The life of a light bulb is normally distributed with a life of 1025 hours and a standard deviation of 75 hours.
1. What is the probability that the lightbulb will last 930 hours or less?
2. What is the probability that the lightbulb will last 820 hours or less?
3. What is the probability that the lightbulb will last longer than 1040 hours?
QUESTION 2 Research Question, Constructing data table and calculating probabilities
14 marks - 5 for 1, 3 for 2, 6 for 3
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 main source of household income of the Australian population. Type of household income is broken down into employee income, own unincorporated business income and other income.
2. Then using Excel, prepare a table of population numbers (not percentages) by type of household income (in the columns) and age (in the rows). Break age into about 6 standard groups, eg, 15-24, 25-34, 35-44, 45-54, 55-64 and 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 earns employee income.
• The probability that any person selected at random from the population is aged between 15 and 34.
• The joint probability that any person selected at random from the population has own unincorporated business income and aged between 25 and 44.
• The conditional probability that any person selected at random from the population is 35 or under given that the person has employee income.
QUESTION 3 Statistical Decision Making and Quality Control
Show all calculations and reasoning.
14 marks - 2 for a (1), 2 for a (2), 3 for a (3), 3 for a (4), 4 for b.
a) Colonial Electric is a large company that produces lightbulbs and other electrical appliances. One particular lightbulb is supposed to have an average life of about 1,000 hours before it burns out. Periodically the company will test 5 of these and measure the average time before these burn out. The following table gives the result of 10 such samples:
Sample 1 2 3 4 5 6 7 8 9 10
Mean 979 1087 1080 934 1072 1007 952 986 1063 958
Range 50 94 57 65 135 134 101 98 145 84
1. What is the overall average of these means? What is the average range?
2. What are the upper and lower control limits for a 99.7% control chart for the mean?
3. Does this process appear to be in control? Explain.
4. Explain why a process can be out of control even though all the samples fall within the upper and lower control limits.
b) Claire Underwood has been concerned about Machine 8 at the Collard Factory. To make sure that the machine is operating correctly samples are taken and the average and the range of each sample is calculated. Each sample consists of 12 items produced from the machine. Recently, 12 samples were taken and for each the sample range and average were calculated. The sample range and sample average were 1.1 and 46 for the first sample, 1.31 and 45 for the second sample, 0.91 and 46 for the third sample, and 1.1 and 47 for the fourth sample. After the fourth sample the sample averages increased. For the fifth sample the range was 1.21, and the average was 48; for sample 6, it was 0.82 and 47, for sample 7 it was 0.86 and 50, for sample 8 it was 1.11 and 49. After the eight sample the sample average continued to increase never getting below 50. For sample 9 the range and average were 1.12 and 51; for sample 10 they were 0.99 and 52; for sample 11 they were 0.86 and 50 and for sample 12 they were 1.2 and 52.
Although Claire’s boss wasn’t overly concerned, Claire was. During installation the supplier had set a value of 47 for the process average and an average range of 1.0. It was Claire’s feeling that something was definitely wrong with machine number 8. Do you agree? Explain your view.
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:
1. Present answers in the same sequence as the questions set.
2. 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 Appendix 1.
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